Core Mathematics

Question 1

1In a right-angled triangle, sin θ = 5/13. Find cos θ.

Easy

A. 8/13 B. 5/12 C. 12/13 D. 13/12

Question 2

2If tan θ = 8/15 and θ is acute, find sin θ + cos θ.

Hard

A. 7/17 B. 17/23 C. 1 D. 23/17

Question 3

3In a right-angled triangle, the side opposite θ is 3 and the hypotenuse is 5. What is cos θ?

Easy

A. 3/4 B. 3/5 C. 4/5 D. 5/4

Question 4

4The magnitude of the vector (5, 12) is

Easy

A. 17 B. 13 C. 7 D. 60

Question 5

5Find the magnitude of the vector (6, −8).

Easy

A. 100 B. 14 C. 10 D. 2

Question 6

6A vector starts at (1, 2) and ends at (4, 6). How long is it?

Easy

A. √13 B. 25 C. 7 D. 5

Question 7

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

Hard

A. 25 B. 7 C. √65 D. 5

Question 8

8If p = (3, −1) and q = (−2, 5), find 3p + 2q.

Hard

A. (1, 4) B. (5, 7) C. (13, −13) D. (−5, 7)

Question 9

9What is the exact value of sin 30°?

Easy

A. √2/2 B. 1 C. 1/2 D. √3/2

Question 10

10If tan θ = 1 and θ is acute, find θ.

Easy

A. 90° B. 45° C. 60° D. 30°