WAEC SSCE - General Mathematics - 2021

In the diagram, line \(\overline{EC}\) is a diameter of the circle ABCDE.

If angle ABC equals 158°, find ?ADE

In the diagram, ?XYZ is produced to T. if |XY| = |ZY| and ?XYT = 40°, find ?XZT

A cone has a base radius of 8cm and height 11cm. calculate , correct to 2d.p, the curved surface area

If 4x+2y=16 and 6x-2y=4 , find the value of (y-x).

Simplify: (11\(_{two}\))\(^2\)

What number should be subtracted from the sum of 2 \(\frac{1}{6}\) and 2\(\frac{7}{12}\) to give 3\(\frac{1}{4}\)?

Find, correct to two decimal, the mean of 1\(\frac{1}{2}\), 2\(\frac{2}{3}\), 3\(\frac{3}{4}\), 4\(\frac{4}{5}\), and 5\(\frac{5}{6}\).

From a point T, a man moves 12km due west and then moves 12km due south to another point Q. Calculate the bearing of T from Q.

The equation of a line is given as 3 x - 5y = 7. Find its gradient (slope)

Answer Details

The equation of a line in the slope-intercept form is y = mx + c, where m is the gradient (slope) of the line and c is the y-intercept. However, the given equation of the line is not in the slope-intercept form, but in the standard form. To find the slope of the line, we need to rewrite the equation in the slope-intercept form. We can do this by solving the equation for y: 3x - 5y = 7 -5y = -3x + 7 y = (3/5)x - 7/5 Comparing this with the slope-intercept form, we can see that the gradient (slope) of the line is 3/5. Therefore, the answer is 3/5.

If 16 * 2\(^{(x + 1)}\) = 4\(^x\) * 8\(^{(1 - x)}\), find the value of x.

If  \(\frac{2}{x-3}\) - \(\frac{3}{x-2}\) = \(\frac{p}{(x-3)(x -2)}\), find p.

A man will be (x+10)years old in 8years time. If 2years ago he was 63 years., find the value of x

Answer Details

A man will be (x+10) years old in 8years time.

 As at today, he is x + 2 years of age.
 

The man was 63 years old 2 years ago, so he is 63+2=65 now.

8 years from now, he will be 65+8=73.
He will be (x+10) years old when he is 73. So

x+10=73
x=73-10=63

The circumference of a circular track is 9km. A cyclist rides round it a number of times and stops after covering a distance of 302km. How far is the cyclist from the starting point?

A solid brass cube is melted and recast as a solid cone of height h and base radius r. If the height of the cube is h, find r in terms of h.

Factorize 6pq-3rs-3ps+6qr

The diagonal of a rhombus are 12cm and 5cm. calculate its perimeter

 A trader paid import duty of 38 kobo in the naira on the cost of an engine. If a total of #22,800.00 was paid as import duty, calculate the cost of the engine.

Mensah is 5 years old and joyce is thrice as old as mensah. In how many years will joyce be twice as old as Mensah?

make u the subject in x =\(\frac{2u-3}{3u + 2}\)

find the value of (x+y)

\(\overline{XY}\) is a line segments with the coordinates X (- 8,- 12) and Y(p,q). if the midpoint of \(\overline{XY}\)  is (-4,-2) find the coordinates of Y.

Answer Details

The midpoint of a line segment is the point that is exactly halfway between the two endpoints of the segment. To find the midpoint, we take the average of the x-coordinates and the y-coordinates of the endpoints. So, for line segment XY with endpoints X (-8,-12) and Y (p,q), the midpoint is (-4,-2). Therefore, the average of the x-coordinates of X and Y is -4: (-8 + p)/2 = -4 Solving for p, we find: p = -8 + 2 * -4 = 0 Similarly, the average of the y-coordinates of X and Y is -2: (-12 + q)/2 = -2 Solving for q, we find: q = -12 + 2 * -2 = 8 Therefore, the coordinates of Y are (0,8).

The height of an equilateral triangle of side is 10 3√ cm. calculate its perimeter.

Given that sin x = 3/5, 0 ≤ x ≤ 90, evaluate (tanx + 2cosx)

Find the 5th term of the sequence 2,5,10,17....?

In △LMN, |LM| = 6cm, ∠LNM = x and sin x = sin x = \(\frac{3}{5}\).

Find the area of △LMN 

In the diagram O is the centre of the circle PQRS, ?PQR = 72° and OR is parallel to PS. Find ∠ OPS

A fair die is tossed twice what is the probability of get a sum of at least 10.

consider the statements:

P = All students offering Literature(L) also offer History(H);

Q = Students offering History(H) do not offer Geography(G).

Which of the Venn diagram correctly illustrate the two statements?

The pie chart represents the distribution of fruits on display in the shop if there are 60 apples on display how many oranges are there? 

if tanθ = \(frac{3}{4}\), 180° < θ < 270°, find the value of cosθ.

The distance d between two villages east more than 18 KM but not more than 23KM.

which of these inequalities represents the statements?

For what value of x is \(\frac{4 - 2x}{x + 1}\) undefined.

The sum of the interior angles of a regular polygon with k sides is (3k-10) right angles. Find the size of the exterior angle?

In the diagram, \(\overline{MP}\) is a tangent to the circle NQR, ∠NQR, ∠PNQ = 64 and | \(\overline{RQ}\) | = | \(\overline{RN}\) |. Find the angle market t. 

 A cyclist moved at a speed of Xkm/h for 2 hours. He then increased his speed by 2 km/h for the next 3 hours.

If the total distance covered is 36 km, calculate his initials speed.

Simplify 2√7- 14/√7+7/21

Find The quadratic Equation Whose Roots Are -2q And 5q. 

In the diagram, PQRS is a circle. find the value of x.

Which of the following is not an exterior angle of a regular polygon?

 In the diagram, ∠ABC and ∠BCD are right angles, ∠BAD = t and ∠EDF = 70°. Find the value of t.

find the first quartile of 7,8,7,9,11,8,7,9,6 and 8.

A trapezium of parellel sides 10cm and 21cm and height 8cm is inscribed in a circle of radius 7cm. calculate the area of the region not covered by the trapezium.

π =\(\frac{22}{7}\) 

the table shows the height of 37 players of a basketball team calculates correct to one decimal place the mean height of the players.

If log\(_{10}\) 2 = m and log\(_{10}\) 3 = n, find log\(_{10}\) 24 in terms of m and n.

if p = {-3<x<1} and Q = {-1<x<3}, where x is a real number, find P n Q.

500 tickets were sold for a concert tickets for adults and children were sold at $4.50 and $3.00  respectively if the total receipts for the concerts was $1987.50 how many tickets for adults were sold?

Answer Details

Let's assume that x is the number of tickets sold for adults, and y is the number of tickets sold for children. We know that the total number of tickets sold is 500, so we can write an equation: x + y = 500 We also know that the price of an adult ticket is $4.50 and the price of a child ticket is $3.00. So we can write another equation based on the total receipts: 4.5x + 3y = 1987.5 Now we have two equations with two unknowns, and we can solve for x, the number of adult tickets sold. One way to do this is to use the first equation to solve for y: y = 500 - x Then we can substitute this expression for y into the second equation: 4.5x + 3(500 - x) = 1987.5 Simplifying and solving for x: 4.5x + 1500 - 3x = 1987.5 1.5x = 487.5 x = 325 So the number of adult tickets sold is 325. Therefore, the correct answer is option (A): 325.

correct 0.007985 to three significant figures.

A box contains 40 identical balls of which 10 are red and 12 are blue. if a ball is selected at random from the box what is the probability that it is neither red nor blue?

Solve: 2\(^{√2x + 1}\) = 32

(a) Mr Sarfo borrowed $25,000 from Afiak financial services at 21% simple interest per annum for 3 years if he was able to pay back the loan in two years at equal yearly installments how much did he pay each year?

(b) Two consecutive numbers are such that the sum of thrice the smaller and twice the larger is 17.

find correct through three significant figures the smaller number as a percentage of the sum of the two numbers

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A man left town am at 10:00 AM and traveled by car to town N at an average speed of 72 km/h.

He spent 2hours for a meeting and returned through town M by bus at an average speed of 40KM/H. 

If the distance covered by the bus was 2km longer than that of the car and he arrived at town M at 1 :55PM.

calculate distance from M to N.

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The table shows the distribution of the number of hours per day spent in studying by 50 students.

Calculate, correct to two decimal places,

the: (a) mean; (b) standard deviation.

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(a) Copy and complete the table of values for the relation y=2x\(^2\) - x - 2 for 4 ≤ x ≤ 4.

 (b) Using a scale of 2 cm to 1 unit on the x-axis and 2 cm to 5 units on the y-axis, draw the graph of  y = 2x\(^2\) - x - 2 for 4 ≤ x ≤ 4.

(c) On the same axes, draw the graph of y = 2x + 3.

(d) Use the graph to find the: (i) roots of the equation 2x-3r-5 0; (i) range of values of x for which 2x\(^2\) -x - 2<0.

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In the diagram, PQRS is a circle.  $\overline{|��|}$ =  $\overline{|��|}$. ∠SPR = 26° and the interior angles of PQS are in the ratio 2:3 :3.

Calculate: (i) PQR; (ii) RPQ; (iii) PRQ

(b) The coordinates of two points P and Q in a plane are (7, 3) and (5, x) respectively, where X is a real number.

If |PQ| = 29 units, find the value of x.

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In the diagram, \(\overline{AD}\) is a diameter of a circle with Centre O. If ABD is a triangle in a semi-circle ∠OAB=34",

find: (a) ∠OAB (b) ∠OCB

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(a) A man shared his property among his children as follows:

Represent the information on a pie chart

(b) A box contains 5 red, 3 green and 4 blue identical beads. Calculate the probability th a girl takes away two red beads, one after the other, from the box.

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.(a) In a class of 80 students,\(\frac{3}{4}\) study Biology and \(\frac{3}{5}\) study Physics.

If each student studies at least one of the subjects: (i) draw a Venn diagram to represent this information

(ii) how many students study both subjects

(iii) find the fraction of the class that study Biology but not Physics.

(b) Johnson and Jocatol Ltd. owned a business office with floor measuring 15m by 8 m which was to be carpeted.

The cost of carpeting was Gh¢ 890.00 per square metre. If a total of GH 216,120.00 was spent on painting and carpeting, how much was the cost of painting? 

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(a) On Sam's first birthday celebration, his grandfather deposited an amount of S 1,000.00 in a bank compound at 4 % interest annually.

Find how much is in the account if Sam is 4 years old.

In the diagram, ABCD are points on the circle centre O. If |AB| = |BC| and ∠ADC= 50°, find ∠BAD.

(a) Amount at end of the 2nd year = \(\frac{104}{100}\) x $1000

= $1,040.00

Amount at end of 3rd year = \(\frac{104}{100}\) x $1040

= $1,081.60

Amount at end of 4th year = \(\frac{104}{100}\) x $1081.6

= $1,124.86

(b) ∠ADC + ∠DCA+ ∠CAD = 180°

50° + 90°+ ∠CAD = 180° 

∠CAD = (180 - 140)° 

= 40

∠ADC + ∠ABC = 180°

  50° + ∠ABC = 180°

∠ABC =130°

∠BAC+ ∠BCA + ∠ABC = 180°

  But ∠BAC = ∠BCA

2∠BAC+ ∠130° = 180°

2 ∠BAC=50° 

∠BAC = 25°

∠BAD = ∠CAD + ∠BAC

= 40°+25°  = 65° 

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.(a) In APQR, ∠PQR= 90°. If its area is 216cm\(^2\) and |PQ|:|QR| is 3:4, find |PR|.

(b) The present ages of a man and his son are 47 years and 17 years respectively. In how many years would the man's age be twice that of his son?

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In the diagram, \(\overline{PQ//RS}\) is a trapezium with QR//PS. U and T are points on \(\overline{PS}\) such that \(\overline{|PU|}\) = 5 cm,

\(\overline{|QU|}\) = 12 cm and ?PUQ= ?STR =90°. If the area of PQR = 20 cm\(^2\),

calculate, correct to the nearest whole number, the:

(a) perimeter; (b) area; of the trapezium

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The points X, Y and Z are located such that Y is 15 km south of X, Z is 20 km from X on a bearing of 270".

Calculate, correct: (a) two significant figures, |YZ|

(b) The nearest degree, the bearing of Y from Z

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(a) A cottage is on a bearing of 200° and 110° from Dogbe's and Manu's farms respectively. If Dogbe walked 5 km and Manu 3 km from the cottage to their farms, find, correct to: (i) two significant figures, the distance between the two farms, (ii) the nearest degree, the bearing of Manu's farm from Dogbe's.

(b) A ladder 10 m long leaned against a vertical wall xm high. The distance between the wall and the foot of the ladder is 2 m longer than the height of the wall.

Calculate the value of x

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