Core Mathematics

1Find the perimeter of a sector of angle 30° in a circle of radius 7 cm. (π = 22/7)

2If 2x + y = 36 and x − y = 9, then x = ___.

3Vertically opposite angles are

4Solve simultaneously y = x² and y = 2x + 3. The positive x value is

5Reflect (−3, 4) in the y-axis.

6Find the quadratic equation whose roots are 1 and 5.

7In triangle ABC, b = 8 cm, c = 10 cm and A = 100°. Find a, to 1 decimal place.

8Solve 5x + 6 < 16.

9Find the equation of the line through (1, 2) and (3, 6).

10Find |p| if p = (5, −12).

11In a right triangle, the side opposite 30° is 4 cm. The hypotenuse is

12If OA = (3, 4) and OB = (7, 1), find |AB|.

136 workers take 10 days to build a wall. How long would 4 workers take, working at the same rate?

14In a class of 35 pupils, 17 study French (F), 17 study Twi (T) and 16 study Ewe (E). 7 study F and T, 7 study F and E, 9 study T and E, and 4 study all three. How many study French only?

15Which point satisfies x + y ≤ 5?

16If x * y = xy − x, then 7 * 4 = ___

17An angle and its complement differ by 30°. Find the smaller angle.

18For any angle θ, sin²θ + cos²θ equals

1910 workers can build a wall in 11 days. How long will 11 workers take?

20A shape of area 8 cm² is enlarged by scale factor 2. The area of the image is ___ cm².