BECE 2021 Mathematics Past Questions and Answers

Answer: A. 3
Intersection (∩) are elements you can find in both sets.

n in n(A∩B) means the number of elements. So you count how many elements are in A∩B once you are done finding the elements.

A = {1, 3, 5, 7, 9, 11, 13, 15}
B = {3, 6, 9, 12, 15}
As you can see 3, 9 and 15 are the only elements that can be seen in both the sets A and B

Hence A∩B = {3,9,15}

Since you are asked how many elements (n), you count how many elements are in {3,9,15} and I believe you've counted three

Hence n(A∩B) = 3

Answer: C. 8
Since the set P is equal to the set Q, thus P = Q, it means all the elements in P is in Q and all the elements in Q is also in P. So you simply have to find which element is in P but not in Q.

P = {4, 8, 12, 16, 20}

Q = {16, 4, 12, k, 20}

Since the elements of P are arranged from the smallest to the largest, let's arrange Q too as well

⇒ Q = {4, k, 12, 16, 20}

P = {4, 8, 12, 16, 20}

As you can see the missing element (k) in Q is 8

Answer: C. 7350
The significant digits of a number are the digits that have meaning or contribute to the value of the number. Sometimes they are also called significant figures.

Which digits are significant?

There are some basic rules that tell you which digits in a number are significant:
• All non-zero digits are significant
• Any zeros between significant digits are also significant
• Trailing zeros to the right of a decimal point are significant

7352.4658 has 8 significant figures (7,3,5,2,4,6,5 and 8). Count from the left, three times to land on the three significant figure. If the next digit is 5 or more, you add 1 to the digit the count ends if not you keep that digit and replace the remaining digits by zeros till the decimal point.

| FIGURES | ONE | TWO | THREE | REPLACE BY 0 DECIMAL POINT | DECIMAL POINT | DECIMAL POINT | |
|---|---|---|---|---|---|---|---|
| DIGITS | 7 | 3 | 5 | 2 . | . | . | |

⇒ 7352.4658 = 7350 three significant figures

Answer: B. 18
Difference in mathematics means subtraction.

Product means multiplication.

Sum means addition.

Hence difference between (2*d*)$^{2}$ and 2*d*$^{2}$ implies (2*d*)$^{2}$ - 2*d*$^{2}$

NOTE: In (2*d*)$^{2}$ the square (2) is affecting both 2 and d since they are both in a bracket but in 2*d*$^{2}$, the square (2) only affects the d.

2*d* means 2 x d

2*d*$^{2}$ means 2 times d square, thus 2 x d$^{2}$

d$^{2}$ = d x d

Hence 2*d*$^{2}$ = 2 x d x d

In (2*d*)$^{2}$, you can simplify the 2*d* and when done square the result, thus multiply the result by itself.

Since d = 3, substitute 3 into wherever you see d and simplify

2*d* = 2 x d, but d = 3

⇒ 2*d* = 2 x 3 = 6

(2*d*)$^{2}$ = (2 x 3)$^{2}$ = 6$^{2}$ = 6 x 6 = 36

2*d*$^{2}$ = 2 x 3$^{2}$ = 2 x 3 x 3 = 2 x 9 = 18

(2*d*)$^{2}$ - 2*d*$^{2}$ = 36 - 18 = 18

Answer: C. (-3, 5)
Property: Rotations by Multiples of 90 Degrees about the Origin

For a point with coordinates (𝑥,𝑦),the following is true:

| POINT # | RULE |
|---|---|
| 1 | A rotation of 90 degrees results in a point with coordinates (−𝑦,𝑥) |
| 2 | A rotation of 180 degrees results in a point with coordinates (−𝑥,−𝑦) |
| 3 | A rotation of 270 degrees results in a point with coordinates (𝑦,−𝑥) |
| 4 | A rotation of 360 degrees results in a point with coordinates (𝑥,𝑦) |
| 5 | A rotation with a positive degree value indicates a counterclockwise rotation, and a rotation with a negative degree value indicates a clockwise rotation. |
| 6 | A rotation of −90∘ is equivalent to a rotation of 270∘, (360-90) and therefore results in a point with coordinates (𝑦,−𝑥) |
| 7 | A rotation of −180∘ is equivalent to a rotation of 180∘, (360-180) and therefore results in a point with coordinates (−𝑥,−𝑦) |
| 8 | A rotation of −270∘ is equivalent to a rotation of 90∘, (360-270) and therefore results in a point with coordinates (−𝑦,𝑥) |
| 9 | A rotation of −360∘ is equivalent to a rotation of 0∘, (360-360) and therefore results in a point with coordinates (𝑥,𝑦). |

From point 4, rotation of point through 360$^{o}$ about the origin is the same point, hence the image of rotating the point (-3, 5) through 360$^{o}$ will be the same, (-3, 5)