WAEC SSCE - General Mathematics - 2015…

Ibeere 1 Ìròyìn

$\begin{array}{c|c}
Scores & 0 - 4 & 5 - 9 & 10 - 14\\
\hline Frequency & 2 & 1 & 2\end{array}$

The table shows the distribution of the scores of some students in a test. Calculate the mean scores.

5.6

6.2

6.6

7.0 Ìdáhùn tó tọ́

Awọn alaye Idahun

Ka ìwé ẹ̀kọ́ nípa Integration (JAMB)

Ka ìwé ẹ̀kọ́ nípa Statistics (WAEC)

Integration

Statistics

Wo Idahun

Ibeere 2 Ìròyìn

Two angles of a pentagon are in the ratio 2:3. The others are 60^o each. Calculate the smaller of the two angles

72^o

100^o

120^o

144^o Ìdáhùn tó tọ́

Awọn alaye Idahun

Let's call the two angles that are in the ratio 2:3 as "2x" and "3x". The sum of the interior angles of a pentagon is given by the formula (5-2) x 180 degrees = 540 degrees. Since the other three angles are all 60 degrees each, we can find the sum of those angles by multiplying 60 by 3, which gives us 180 degrees. Now we can set up an equation to solve for the unknown angle, which is 2x + 3x. 2x + 3x + 180 = 540 Simplifying this equation, we get: 5x + 180 = 540 Subtracting 180 from both sides, we get: 5x = 360 Dividing both sides by 5, we get: x = 72 So the smaller angle, which is 2x, is equal to 2 times 72, which is 144 degrees. Therefore, the correct answer is 144 degrees.

Ka ìwé ẹ̀kọ́ nípa Angles (WAEC)

Angles

Wo Idahun

Ibeere 3 Ìròyìn

The sum 11011₂, 1111₂ and 10_m10_n0₂. Find the value of m and n.

m = 0, n = 0

m = 1, n = 0

m = 0, n = 1 Ìdáhùn tó tọ́

m = 1, n = 1

Awọn alaye Idahun

Ka ìwé ẹ̀kọ́ nípa Number Bases (WAEC)

Number Bases

Wo Idahun

Ibeere 4 Ìròyìn

Find the 7^th term of the sequence: 2, 5, 10, 17, 6,...

50 Ìdáhùn tó tọ́

Awọn alaye Idahun

Ka ìwé ẹ̀kọ́ nípa Sequence And Series (WAEC)

Sequence And Series

Wo Idahun

Ibeere 5 Ìròyìn

The angle of elevation of an aircraft from a point K on the horizontal ground 30$\alpha$. If the aircraft is 800m above the ground, how far is it from K?

400.00m

692.82m

923.76m

1,600.99m Ìdáhùn tó tọ́

Awọn alaye Idahun

Ka ìwé ẹ̀kọ́ nípa Introductory Calculus (WAEC)

Ka ìwé ẹ̀kọ́ nípa Coordinate Geometry (WAEC)

Introductory Calculus

Coordinate Geometry

Wo Idahun

Ibeere 6 Ìròyìn

The probability that kebba, Ebou and Omar will hit a target are $\frac{2}{3}$, $\frac{3}{4}$ and $\frac{4}{5}$ respectively. Find the probability that only Kebba will hit the target.

$\frac{2}{5}$

$\frac{7}{60}$

$\frac{1}{30}$ Ìdáhùn tó tọ́

$\frac{1}{60}$

Awọn alaye Idahun

The probability that only Kebba will hit the target means that Kebba hits the target and the other two miss the target. We can find this probability by multiplying the probability of Kebba hitting the target with the probability of Ebou missing the target and the probability of Omar missing the target. Probability that only Kebba hits the target = Probability of Kebba hitting the target × Probability of Ebou missing the target × Probability of Omar missing the target = $\frac{2}{3}$ × $\frac{1}{4}$ × $\frac{1}{5}$ = $\frac{2}{3\times4\times5}$ = $\frac{1}{30}$ Therefore, the probability that only Kebba will hit the target is $\frac{1}{30}$.

Ka ìwé ẹ̀kọ́ nípa Probability (WAEC)

Probability

Wo Idahun

Ibeere 7 Ìròyìn

The area of a rhombus is 110 cm$^2$. If the diagonals are 20 cm and (2x + 1) cm long, find the value of x.

5.0 Ìdáhùn tó tọ́

4.0

3.0

2.5

Awọn alaye Idahun

Ka ìwé ẹ̀kọ́ nípa Areas (WAEC)

Ka ìwé ẹ̀kọ́ nípa Angles (WAEC)

Areas

Angles

Wo Idahun

Ibeere 8 Ìròyìn

Find the equation whose roots are $\frac{3}{4}$ and -4

4x² - 13x + 12 = 0

4x² - 13x - 12 = 0

4x² + 13x - 12 = 0 Ìdáhùn tó tọ́

4x² + 13x + 12 = 0

Awọn alaye Idahun

If a quadratic equation has roots p and q, then it can be expressed in the factored form as:

(x - p)(x - q) = 0

Expanding this equation, we get:

x² - (p + q)x + pq = 0

In this case, the roots are given as $\frac{3}{4}$ and -4. Thus, the equation can be expressed as:

(x - \(\frac{3}{4}\))(x + 4) = 0

Expanding this equation, we get:

x² + (4 - \(\frac{3}{4}\))x - 3 = 0

Multiplying throughout by 4 to eliminate fractions, we get:

4x² + 13x - 12 = 0

Therefore, the equation whose roots are $\frac{3}{4}$ and -4 is 4x² + 13x - 12 = 0.

Hence, the answer is 4x² + 13x - 12 = 0.

Wo Idahun

Ibeere 9 Ìròyìn

Make K the subject of the relation T = $\sqrt{\frac{TK - H}{K - H}}$

K = $\frac{H(T^2 - 1)}{T^2 - T}$ Ìdáhùn tó tọ́

K = $\frac{HT}{(T - 1)^2}$

K = $\frac{H(T^2 + 1)}{T}$

K = $\frac{H(T - 1)}{T}$

Awọn alaye Idahun

Ka ìwé ẹ̀kọ́ nípa Algebraic Fractions (WAEC)

Ka ìwé ẹ̀kọ́ nípa Quadratic Equations (WAEC)

Algebraic Fractions

Quadratic Equations

Wo Idahun

Ibeere 10 Ìròyìn

If 2ⁿ = y, Find 2$^{(2 + \frac{n}{3})}$

4y$^\frac{1}{3}$ Ìdáhùn tó tọ́

4y$^-3$

2y$^\frac{1}{3}$

2y$^-3$

Awọn alaye Idahun

We know that 2$^n$ = y. Therefore, 2$^{(2 + \frac{n}{3})}$ can be written as 2$^2$ × 2$^{\frac{n}{3}}$ = 4 × 2$^{\frac{n}{3}}$. Substituting 2$^n$ = y in the above equation, we get: 2$^{(2 + \frac{n}{3})}$ = 4y$^\frac{1}{3}$ Therefore, the answer is (a) 4y$^\frac{1}{3}$.

Ka ìwé ẹ̀kọ́ nípa Indices (WAEC)

Ka ìwé ẹ̀kọ́ nípa Logarithms (WAEC)

Indices

Logarithms

Wo Idahun

Ibeere 11 Ìròyìn

PQRT is square. If x is the midpoint of PQ, Calculate correct to the nearest degree, LPXS

53^o

55^o

63^o Ìdáhùn tó tọ́

65^o

Awọn alaye Idahun

Wo Idahun

Ibeere 12 Ìròyìn

Factorize completely: 6ax - 12by - 9ay + 8bx

(2a - 3b)(4x + 3y)

(3a + 4b)(2x - 3y) Ìdáhùn tó tọ́

(3a - 4b)(2x + 3y)

(2a + 3b)(4x -3y)

Awọn alaye Idahun

Ka ìwé ẹ̀kọ́ nípa Algebraic Expressions (WAEC)

Algebraic Expressions

Wo Idahun

Ibeere 13 Ìròyìn

A farmer uses $\frac{2}{5}$ of his land to grow cassava, $\frac{1}{3}$ of the remaining for yam and the rest for maize. Find the part of the land used for maize

$\frac{2}{15}$

$\frac{2}{5}$ Ìdáhùn tó tọ́

$\frac{2}{3}$

$\frac{4}{5}$

Awọn alaye Idahun

Let's assume the farmer has 15 parts of land. The fraction of land used for cassava is $\frac{2}{5}$ of 15, which is 6 parts. The remaining land is 15 - 6 = 9 parts. The fraction of the remaining land used for yam is $\frac{1}{3}$ of 9, which is 3 parts. Therefore, the part of the land used for maize is the remaining land after cassava and yam are planted, which is 9 - 3 = 6 parts. So the fraction of the land used for maize is $\frac{6}{15}$, which simplifies to $\frac{2}{5}$. Therefore, the answer is option (B) $\frac{2}{5}$.

Ka ìwé ẹ̀kọ́ nípa Fractions, Decimals And Approximations (WAEC)

Ka ìwé ẹ̀kọ́ nípa Number Bases (WAEC)

Fractions, Decimals And Approximations

Number Bases

Wo Idahun

Ibeere 14 Ìròyìn

In the diagram, VW//YZ, |WX| = 6cm, |XY| = 16cm, |YZ| = 20cm and |ZX| = 12cm. Calculate |VX|

3cm

4cm

6cm

8cm Ìdáhùn tó tọ́

Awọn alaye Idahun

Wo Idahun

Ibeere 15 Ìròyìn

Given that logx 64 = 3, evaluate x log$_2$8

12 Ìdáhùn tó tọ́

Awọn alaye Idahun

Ka ìwé ẹ̀kọ́ nípa Modular Arithmetic (WAEC)

Ka ìwé ẹ̀kọ́ nípa Logarithms (WAEC)

Modular Arithmetic

Logarithms

Wo Idahun

Ibeere 16 Ìròyìn

If $\frac{27^x \times 3^{1 - x}}{9^{2x}} = 1$, find the value of x.

$\frac{1}{2}$ Ìdáhùn tó tọ́

-$\frac{1}{2}$

-1

Awọn alaye Idahun

Ka ìwé ẹ̀kọ́ nípa Number Bases (WAEC)

Ka ìwé ẹ̀kọ́ nípa Indices (WAEC)

Number Bases

Indices

Wo Idahun

Ibeere 17 Ìròyìn

Describe the shaded portion in the diagram

P' $\cap$ Q $\cap$ R' Ìdáhùn tó tọ́

(P' $\cap$ R)' $\cap$ R

P' $\cap$ Q $\cap$ R

(P $\cap$ Q)' $\cap$ R

Awọn alaye Idahun

The shaded portion in the diagram represents the set of elements that belong to the complement of P and the intersection of Q and R. In other words, it represents the set of elements that are not in P, but are in both Q and R. Therefore, the correct answer is P' $\cap$ Q $\cap$ R'.

Ka ìwé ẹ̀kọ́ nípa Logical Reasoning (WAEC)

Ka ìwé ẹ̀kọ́ nípa Sets (JAMB)

Logical Reasoning

Sets

Wo Idahun

Ibeere 18 Ìròyìn

The population of students in a school is 810. If this is represented on a pie chart, calculate the sectoral angle for a class of 7 students

32^o Ìdáhùn tó tọ́

45^o

60^o

75^o

Awọn alaye Idahun

To find the sectoral angle for a class of 7 students, we first need to calculate what percentage of the total population they represent: Percentage of class of 7 students = (Number of students in the class / Total population) x 100% Percentage of class of 7 students = (7 / 810) x 100% Percentage of class of 7 students = 0.864% (rounded to three decimal places) Next, we need to convert this percentage to an angle of the pie chart. We know that a full circle is 360 degrees, and the percentage of the class of 7 students represents a certain portion of this circle. We can use the following formula to calculate the sectoral angle: Sectoral angle = Percentage of class of 7 students x 360 degrees Plugging in the percentage we calculated earlier, we get: Sectoral angle = 0.864% x 360 degrees Sectoral angle ≈ 3.11 degrees (rounded to two decimal places) Therefore, the sectoral angle for a class of 7 students in the pie chart is approximately 3.11 degrees. So, the correct option is (a) 32^o.

Ka ìwé ẹ̀kọ́ nípa Representation Of Data (JAMB)

Ka ìwé ẹ̀kọ́ nípa Sets (JAMB)

Ka ìwé ẹ̀kọ́ nípa Mensuration (JAMB)

Representation Of Data

Sets

Mensuration

Wo Idahun

Ibeere 19 Ìròyìn

In the diagram, O is the centre. If PQ//RS and ∠ONS = 140°, find the size of ∠POM.

40^o Ìdáhùn tó tọ́

50^o

60^o

80^o

Awọn alaye Idahun

Ka ìwé ẹ̀kọ́ nípa Euclidean Geometry (JAMB)

Euclidean Geometry

Wo Idahun

Ibeere 20 Ìròyìn

A letter is selected from the letters of the English alphabet. What is the probability that the letter selected is from the word MATHEMATICS?

$\frac{9}{13}$

$\frac{11}{26}$

$\frac{4}{13}$ Ìdáhùn tó tọ́

$\frac{1}{26}$

Awọn alaye Idahun

The word MATHEMATICS contains the letters A, C, E, H, I, M, S, and T. Since there are 26 letters in the English alphabet, the probability of selecting any letter from the alphabet is 1 out of 26. Out of the letters in the word MATHEMATICS, there are 8 letters, so the probability of selecting a letter from the word MATHEMATICS is 8 out of 26. Therefore, the probability of selecting a letter from the word MATHEMATICS is: $$\frac{8}{26}=\frac{4}{13}$$ Therefore, the correct answer is option (C).

Ka ìwé ẹ̀kọ́ nípa Probability (WAEC)

Ka ìwé ẹ̀kọ́ nípa Surds (radicals) (WAEC)

Probability

Surds (radicals)

Wo Idahun

Ibeere 21 Ìròyìn

Calculate the mean deviation of 5, 3, 0, 7, 2, 1

0.0

2.0 Ìdáhùn tó tọ́

2.5

3.0

Awọn alaye Idahun

To find the mean deviation, we need to first calculate the mean of the given set of numbers: Mean = (5 + 3 + 0 + 7 + 2 + 1) / 6 = 18 / 6 = 3 Next, we need to find the absolute deviation of each number from the mean: |5 - 3| = 2 |3 - 3| = 0 |0 - 3| = 3 |7 - 3| = 4 |2 - 3| = 1 |1 - 3| = 2 To calculate the mean deviation, we add up these absolute deviations and divide by the number of numbers: Mean deviation = (2 + 0 + 3 + 4 + 1 + 2) / 6 = 12 / 6 = 2 Therefore, the answer is option (B) 2.0.

Ka ìwé ẹ̀kọ́ nípa Measures Of Location (JAMB)

Measures Of Location

Wo Idahun

Ibeere 22 Ìròyìn

Tom will be 25 years old in n years' time. If he is 5 years younger than Bade's present age.

(30 - n)years Ìdáhùn tó tọ́

(20 - n)years

(25 - n)years

(30 + n)years

Awọn alaye Idahun

Ka ìwé ẹ̀kọ́ nípa Solution Of Linear Equations (WAEC)

Ka ìwé ẹ̀kọ́ nípa Circles (WAEC)

Solution Of Linear Equations

Circles

Wo Idahun

Ibeere 23 Ìròyìn

In the diagram, O is the centre, $\bar{RT}$ is a diameter, < PQT = 33$^o$ and <TOS = 76$^o$. Using the diagram, calculate the value of angle PTR.

73^o

67^o

57^o Ìdáhùn tó tọ́

37^o

Awọn alaye Idahun

Ka ìwé ẹ̀kọ́ nípa Number Bases (WAEC)

Ka ìwé ẹ̀kọ́ nípa Coordinate Geometry (WAEC)

Number Bases

Coordinate Geometry

Wo Idahun

Ibeere 24 Ìròyìn

If $\frac{\sqrt{2} + \sqrt{3}}{\sqrt{3}}$ is simplified as m + n$\sqrt{6}$, find the value of (m + n)

$\frac{1}{3}$

$\frac{2}{3}$

1$\frac{1}{3}$ Ìdáhùn tó tọ́

1$\frac{2}{3}$

Awọn alaye Idahun

Ka ìwé ẹ̀kọ́ nípa Surds (radicals) (WAEC)

Surds (radicals)

Wo Idahun

Ibeere 25 Ìròyìn

Which of the following is used to determine the mode of a grouped data?

Bar chart

Frequency polygon

Ogive

Histogram Ìdáhùn tó tọ́

Awọn alaye Idahun

Ka ìwé ẹ̀kọ́ nípa Representation Of Data (JAMB)

Ka ìwé ẹ̀kọ́ nípa Integration (JAMB)

Representation Of Data

Integration

Wo Idahun

Ibeere 26 Ìròyìn

In the diagram, O is the centre, $\bar{RT}$ is a diameter, < PQT = 33$^o$ and < TOS = 76$^o$. Using the diagram, find the size of angle PRS.

76^o

71^o Ìdáhùn tó tọ́

38^o

33^o

Awọn alaye Idahun

Ka ìwé ẹ̀kọ́ nípa Circles (WAEC)

Circles

Wo Idahun

Ibeere 27 Ìròyìn

A trader bought an engine for $15,000.00 outside Nigeria. If the exchange rate is $0.075 to N1.00, how much did the engine cost in Naira?

N250,000.00

N200,000.00 Ìdáhùn tó tọ́

N150,000.00

N100,000.00

Awọn alaye Idahun

Ka ìwé ẹ̀kọ́ nípa Positive And Negative Integers, Rational Numbers (WAEC)

Ka ìwé ẹ̀kọ́ nípa Modular Arithmetic (WAEC)

Positive And Negative Integers, Rational Numbers

Modular Arithmetic

Wo Idahun

Ibeere 28 Ìròyìn

If m = 4, n = 9 and r = 16., evaluate $\frac{m}{n}$ - 1$\frac{7}{9}$ + $\frac{n}{r}$

1$\frac{5}{16}$

1$\frac{1}{16}$

$\frac{5}{16}$

- 1$\frac{37}{48}$ Ìdáhùn tó tọ́

Awọn alaye Idahun

Ka ìwé ẹ̀kọ́ nípa Fractions, Decimals And Approximations (WAEC)

Fractions, Decimals And Approximations

Wo Idahun

Ibeere 29 Ìròyìn

In a circle radius rcm, a chord 16$\sqrt{3}cm$ long is 10cmfrom the centre of the circle. Find, correct to the nearest cm, the value of r

22cm

17cm Ìdáhùn tó tọ́

16cm

15cm

Awọn alaye Idahun

In a circle, a radius is a line segment that connects the center of the circle to any point on the circle. A chord is a line segment that connects two points on a circle. Given that a chord of length 16$\sqrt{3}cm$ is 10cm from the center of the circle, we can use the Pythagorean theorem to find the length of the radius. First, we draw a line from the center of the circle perpendicular to the chord, creating a right triangle with the radius, the perpendicular line, and half the chord length (which is $8\sqrt{3}$ cm). Using the Pythagorean theorem: \begin{align*} r^2 &= (8\sqrt{3})^2 + 10^2 \\ r^2 &= 192 + 100 \\ r^2 &= 292 \\ r &\approx \sqrt{292} \\ r &\approx 17 \text{ cm} \end{align*} Rounding to the nearest whole number, we get the answer of 17cm. Therefore, the correct option is (b) 17cm.

Ka ìwé ẹ̀kọ́ nípa Circles (WAEC)

Ka ìwé ẹ̀kọ́ nípa Triangles And Polygons (WAEC)

Circles

Triangles And Polygons

Wo Idahun

Ibeere 30 Ìròyìn

In the diagram, PTR is a tangent to the centre O. If angles TON = 108°, Calculate the size of angle PTN

132^o

126^o Ìdáhùn tó tọ́

108^o

102^o

Awọn alaye Idahun

Ka ìwé ẹ̀kọ́ nípa Circles (WAEC)

Ka ìwé ẹ̀kọ́ nípa Algebraic Expressions (WAEC)

Ka ìwé ẹ̀kọ́ nípa Euclidean Geometry (JAMB)

Ka ìwé ẹ̀kọ́ nípa Triangles And Polygons (WAEC)

Circles

Algebraic Expressions

Euclidean Geometry

Triangles And Polygons

Wo Idahun

Ibeere 31 Ìròyìn

The volume of a cone of height 3cm is 38$\frac{1}{2}$cm³. Find the radius of its base. [Take $\pi = \frac{22}{7}$]

3.0cm

3.5cm Ìdáhùn tó tọ́

4.0cm

4.5cm

Awọn alaye Idahun

Wo Idahun

Ibeere 32 Ìròyìn

In the diagram, PQ//RT, QR//Su,

134^o

132^o Ìdáhùn tó tọ́

96^o

48^o

Awọn alaye Idahun

Ka ìwé ẹ̀kọ́ nípa Angles And Intercepts On Parallel Lines (WAEC)

Ka ìwé ẹ̀kọ́ nípa Triangles And Polygons (WAEC)

Angles And Intercepts On Parallel Lines

Triangles And Polygons

Wo Idahun

Ibeere 33 Ìròyìn

$\begin{array}{c|c}
x & 0 & 1\frac{1}{4} & 2 & 4\\
\hline
y & 3 & 5\frac{1}{2} & &
\end{array}$
The table given shows some values for a linear graph. Find the gradient of the line

2 Ìdáhùn tó tọ́

Awọn alaye Idahun

To find the gradient of a line, we need to calculate the change in y divided by the change in x between two points on the line. Let's choose two points on the line from the given table. We can select the points (0,3) and (2,y), where y is the value of y for x = 2. The change in y is y - 3, and the change in x is 2 - 0 = 2. Therefore, the gradient of the line is: gradient = change in y / change in x = (y - 3) / 2 We don't know the value of y yet, but we can use the other point on the line to find it. Using the points (1.25, 5.5) and (2, y), we get: gradient = (y - 5.5) / (2 - 1.25) = (y - 5.5) / 0.75 Setting the two expressions for the gradient equal to each other, we get: (y - 3) / 2 = (y - 5.5) / 0.75 Solving for y gives: y = 7 Therefore, the value of y for x = 2 is 7, and the gradient of the line is: gradient = (y - 3) / 2 = (7 - 3) / 2 = 2 So the answer is 2, and the gradient of the line is 2. In simple terms, the gradient of a line tells us how steep the line is. If the gradient is positive, the line is sloping upwards from left to right. If the gradient is negative, the line is sloping downwards from left to right. The larger the absolute value of the gradient, the steeper the line.

Ka ìwé ẹ̀kọ́ nípa Graphs Of Linear And Quadratic Functions (WAEC)

Graphs Of Linear And Quadratic Functions

Wo Idahun

Ibeere 34 Ìròyìn

If {X: 2 d- x d- 19; X integer} and 7 + x = 4 (mod 9), find the highest value of x

15 Ìdáhùn tó tọ́

Awọn alaye Idahun

To solve this problem, we need to use the given conditions to find the possible values of x and then determine the highest value among them. From the first condition, we know that x is an integer between 2 and 19 (inclusive) and can be represented as {X: 2 d- x d- 19; X integer}. This means that x can take on any of the following values: 2, 3, 4, ..., 18, 19. The second condition tells us that 7 + x is congruent to 4 modulo 9, which can be written as: 7 + x ≡ 4 (mod 9) To solve for x, we can subtract 7 from both sides of the congruence: x ≡ -3 (mod 9) Since we want x to be between 2 and 19, we can add or subtract multiples of 9 to -3 until we get a value within the range of possible values for x. Doing so, we obtain: x ≡ -3 (mod 9) x ≡ 15 (mod 9) Since 15 is the largest value of x that satisfies both conditions, our answer is 15.

Ka ìwé ẹ̀kọ́ nípa Positive And Negative Integers, Rational Numbers (WAEC)

Ka ìwé ẹ̀kọ́ nípa Modular Arithmetic (WAEC)

Positive And Negative Integers, Rational Numbers

Modular Arithmetic

Wo Idahun

Ibeere 35 Ìròyìn

In the diagram, $\bar{OX}$ bisects < YXZ and $\bar{OZ}$ bisects < YZX. If < XYZ = 68^o, calculate the value of < XOZ

68^o

72^o

112^o

124^o Ìdáhùn tó tọ́

Awọn alaye Idahun

Ka ìwé ẹ̀kọ́ nípa Angles And Intercepts On Parallel Lines (WAEC)

Angles And Intercepts On Parallel Lines

Wo Idahun

Ibeere 36 Ìròyìn

Find the value of p if $\frac{1}{4}$p + 3q = 10 and 2p - q = 7

4 Ìdáhùn tó tọ́

-3

-4

Awọn alaye Idahun

Ka ìwé ẹ̀kọ́ nípa Solution Of Linear Equations (WAEC)

Ka ìwé ẹ̀kọ́ nípa Algebraic Expressions (WAEC)

Solution Of Linear Equations

Algebraic Expressions

Wo Idahun

Ibeere 37 Ìròyìn

A trader bought 100 oranges at 5 for N40.00 and 20 for N120.00. Find the profit or loss percent

20% profit

20% loss

25% profit

25% loss Ìdáhùn tó tọ́

Awọn alaye Idahun

Ka ìwé ẹ̀kọ́ nípa Number Bases (WAEC)

Number Bases

Wo Idahun

Ibeere 38 Ìròyìn

Adding 42 to a given positive number gives the same result as squaring the number. Find the number

7 Ìdáhùn tó tọ́

Awọn alaye Idahun

Let's call the unknown number "x". According to the problem, adding 42 to x gives the same result as squaring x. We can write this as an equation: x + 42 = x^2 To solve for x, we can rearrange this equation to get it in standard quadratic form: x^2 - x - 42 = 0 Now we can factor this quadratic equation: (x - 7)(x + 6) = 0 This gives us two possible solutions: x = 7 and x = -6. However, we were given that x is a positive number, so we can discard the negative solution. Therefore, the answer is x = 7. To check our answer, we can substitute x = 7 into the original equation: 7 + 42 = 49 7^2 = 49 So adding 42 to 7 does indeed give the same result as squaring 7.

Wo Idahun

Ibeere 39 Ìròyìn

Simplify: $\frac{3x - y}{xy} - \frac{2x + 3y}{2xy} + \frac{1}{2}$

$\frac{4x + 5y - xy}{2xy}$

$\frac{5y - 4x + xy}{2xy}$

$\frac{5x + 4y - xy}{2xy}$

$\frac{4x - 5y + xy}{2xy}$ Ìdáhùn tó tọ́

Awọn alaye Idahun

To simplify the expression, we first need to find a common denominator for the fractions. The lowest common multiple of the denominators xy and 2xy is 2xy. $\frac{3x - y}{xy} - \frac{2x + 3y}{2xy} + \frac{1}{2} = \frac{3x\cdot2 - y\cdot2}{xy\cdot2} - \frac{2x\cdot1 + 3y\cdot1}{2xy\cdot1} + \frac{1\cdot xy}{2\cdot xy}$ Simplifying further, we get: $\frac{6x - 2y}{2xy} - \frac{2x + 3y}{2xy} + \frac{xy}{2xy}$ Combining like terms, we get: $\frac{4x - 5y + xy}{2xy}$ Therefore, the answer is option D: $\frac{4x - 5y + xy}{2xy}$.

Wo Idahun

Ibeere 40 Ìròyìn

In the given diagram, $\bar{QT}$ and $\bar{PR}$ are straight lines, < ROS = (3n - 20), < SOT = n, < POL = m and < QOL is a right angle. Find the value of n.

35^o Ìdáhùn tó tọ́

40^o

55^o

60^o

Awọn alaye Idahun

Since < QOL is a right angle, we have: < QOT + < SOT = 90^o Since < QOT = 180^o - < POL, we have: < QOT = 180^o - m Substituting into the first equation, we get: 180^o - m + n = 90^o n - m = 90^o - 180^o = -90^o Also, from the diagram, we have: < QOT + < ROS + < SOT = 180^o Substituting < QOT = 180^o - < POL and simplifying, we get: 180^o - m + (3n - 20) + n = 180^o 4n - m = 20 We now have a system of two equations: n - m = -90^o 4n - m = 20 Solving simultaneously, we get: n = 35^o

Ka ìwé ẹ̀kọ́ nípa Algebraic Expressions (WAEC)

Ka ìwé ẹ̀kọ́ nípa Angles And Intercepts On Parallel Lines (WAEC)

Algebraic Expressions

Angles And Intercepts On Parallel Lines

Wo Idahun

Ibeere 41 Ìròyìn

Ada draws the graph of y = x² - x - 2 and y = 2x - 1 on the same axes. Which of these equations is she solving?

x² - x - 3 = 0

x² - 3x - 1 = 0 Ìdáhùn tó tọ́

x² - 3x - 3 = 0

x² + 3x - 1 = 0

Awọn alaye Idahun

Ka ìwé ẹ̀kọ́ nípa Quadratic Equations (WAEC)

Ka ìwé ẹ̀kọ́ nípa Graphs Of Linear And Quadratic Functions (WAEC)

Quadratic Equations

Graphs Of Linear And Quadratic Functions

Wo Idahun

Ibeere 42 Ìròyìn

The rate of consumption of petrol by a vehicle varies directly as the square of the distance covered. If 4 litres of petrol is consumed on a distance of 15km. how far would the vehicle go on 9 litres of petrol?

22$\frac{1}{2}$km Ìdáhùn tó tọ́

30km

33$\frac{1}{2}$km

45km

Awọn alaye Idahun

Since the rate of consumption of petrol varies directly as the square of the distance covered, let's assume that the rate is k$\frac{\text{litres}}{\text{km}^2}$. Then we can write the relationship as: rate of consumption = k(distance covered)$^2$ We are given that when the distance covered is 15 km, the rate of consumption is 4 litres. Substituting these values in the above equation, we get: 4 = k(15)$^2$ k = $\frac{4}{15^2}$ Now, we need to find how far the vehicle can go on 9 litres of petrol. Let's assume that the vehicle can travel a distance of x km on 9 litres of petrol. Using the same equation as before, we get: 9 = $\frac{4}{15^2}$(x)$^2$ Simplifying this equation, we get: x$^2$ = $\frac{9}{\frac{4}{15^2}}$ x$^2$ = 506.25 x = 22.5 Therefore, the vehicle can travel 22.5 km on 9 litres of petrol. So the answer is 22$\frac{1}{2}$km.

Ka ìwé ẹ̀kọ́ nípa Sequence And Series (WAEC)

Ka ìwé ẹ̀kọ́ nípa Ratio, Proportions And Rates (WAEC)

Sequence And Series

Ratio, Proportions And Rates

Wo Idahun

Ibeere 43 Ìròyìn

In the diagram, the shaded part is carpet laid in a room with dimensions 3.5m by 2.2m leaving a margin of 0.5m round it. Find area of the margin

4.7m² Ìdáhùn tó tọ́

4.9m²

5.7m²

5.9m²

Awọn alaye Idahun

Ka ìwé ẹ̀kọ́ nípa Lengths And Perimeters (WAEC)

Lengths And Perimeters

Wo Idahun

Ibeere 44 Ìròyìn

The dimension of a rectangular tank are 2m by 7m by 11m. If its volume is equal to that of a cylindrical tank of height 4cm, calculate the base radius of the cylindrical tank. [Take $\pi = \frac{22}{7}$]

14cm

3$\frac{1}{2}$m Ìdáhùn tó tọ́

1$\frac{3}{4}$m

Awọn alaye Idahun

Ka ìwé ẹ̀kọ́ nípa Volumes (WAEC)

Ka ìwé ẹ̀kọ́ nípa Fractions, Decimals And Approximations (WAEC)

Volumes

Fractions, Decimals And Approximations

Wo Idahun

Ibeere 45 Ìròyìn

The scores of twenty students in a test are as follows: 44, 47, 48, 49, 50, 51, 52, 53, 53, 54, 58, 59, 60, 61, 63, 65, 67, 70, 73, 75. Find the third quartile.

64 Ìdáhùn tó tọ́

Awọn alaye Idahun

Ka ìwé ẹ̀kọ́ nípa Measures Of Dispersion (JAMB)

Measures Of Dispersion

Wo Idahun






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WAEC SSCE - General Mathematics - 2015 (Objective)