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**Question 1**
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*The pie chart illustrate the amount of private time a student spends in a week studying various subjects. use it to answer the question below*

If he sends \(2\frac{1}{2}\) hours week on science, find the total number of hours he studies in a week

**Question 2**
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If \(K\sqrt{28}+\sqrt{63}-\sqrt{7}=0\), find K.

**Answer Details**

We can simplify the given equation as follows: $$K\sqrt{28}+\sqrt{63}-\sqrt{7}=0$$ $$K\sqrt{4\cdot7}+\sqrt{9\cdot7}-\sqrt{7}=0$$ $$2K\sqrt{7}+3\sqrt{7}-\sqrt{7}=0$$ $$2K\sqrt{7}+2\sqrt{7}=0$$ $$2\sqrt{7}(K+1)=0$$ Since $\sqrt{7}$ is not zero, we can divide both sides by $2\sqrt{7}$ to get: $$K+1=0$$ Therefore, $K=-1$. So the answer is (B) -1.

**Question 3**
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Two numbers 24\(_{x}\) and 31\(_y\) are equal in value when converted to base ten. Find the equation connecting x and y

**Question 4**
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From the diagram above. ABC is a triangle inscribed in a circle center O. ?ACB = 40^{o} and |AB| = x cm. calculate the radius of the circle.

**Question 5**
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Which of the following statements is true from the diagram above?

**Question 6**
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If \(x^2 +15x + 50 = ax^2 + bx + c = 0\). Which of the following statement is not true?

**Answer Details**

Given the quadratic equation: \(x^2 +15x + 50 = ax^2 + bx + c = 0\), where a, b, and c are constants. The question is asking which of the following statements is not true. We can first use the quadratic formula to find the values of x in terms of a, b, and c: $$x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$ Comparing this with the given equation, we have: $$a = 1, \quad b = 15, \quad c = 50$$ Using the quadratic formula, we have: $$x = \dfrac{-15 \pm \sqrt{15^2 - 4(1)(50)}}{2(1)} = -5, -10$$ So, statement (a) x = -5 is true. To find out which statement is not true, we can check each option. Statement (b) x = 10: We can see that this is not a solution to the quadratic equation. Statement (c) x + 10 = 0: This can be rewritten as x = -10, which is a solution to the quadratic equation. Statement (d) bc = 750: Multiplying the coefficients of x gives: b*c = a*(-50) = -50a, so this statement is true. Therefore, the statement that is not true is (b) x = 10.

**Question 7**
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In the diagram, PQST and QRST are parallelograms. Calculate the area of the trapezium PRST.

**Question 8**
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Given that m = -3 and n = 2 find the value of \(\frac{3n^2 - 2m^3}{m}\)

**Question 9**
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Describe the locus L shown in the diagram below

**Question 10**
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Simplify \(\frac{2-18m^2}{1+3m}\)

**Answer Details**

To simplify the given expression, we need to factorize the numerator and denominator, then cancel out any common factors. The numerator can be factorized as the difference of two squares: 2 - 18m^2 = 2(1 - 9m^2) = 2(1 + 3m)(1 - 3m) The denominator is already factorized: 1 + 3m Now we can cancel out the common factor of (1 + 3m) from the numerator and denominator: \[\frac{2-18m^2}{1+3m} = \frac{2(1+3m)(1-3m)}{1+3m} = 2(1-3m)\] Therefore, the simplified form of the expression is 2(1-3m).

**Question 12**
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