# Mathematics 2022 Past Questions | WAEC

Evaluate, correct to four significant figures, (573.06 x 184.25).

- A. 105600.00
- B. 105622.00
- C. 105500.00
- D. 105632.00

**Correct Option: Answer is A**

573.06 x 184.25 = 105586.725

Rounding this result to four significant figures, we get:

105600

The rules for significant figures (also known as significant digits) are guidelines used to determine the number of meaningful digits in a number. Here are the main rules:

Non-zero digits are always significant. For example, the number 123 has three significant figures.

Zeros between non-zero digits are always significant. For example, the number 505 has three significant figures.

Leading zeros (zeros to the left of the first non-zero digit) are not significant and are used only to locate the decimal point. For example, the number 0.007 has one significant figure.

Trailing zeros (zeros to the right of non-zero digits) are significant if they are after the decimal point. For example, the number 12.00 has four significant figures.

Trailing zeros that are not after the decimal point are not significant unless they are indicated with a decimal point. For example, the number 1200 has two significant figures, but 1200. has four significant figures.

Exact numbers, such as counting numbers or defined quantities, have an infinite number of significant figures. For example, there are exactly 12 eggs in a dozen.

**2. **Change 432_{five} to a number in base three.

- A. 10100
_{three} - B. 11100
_{three} - C. 11101
_{three} - D. 10110
_{three}

**Correct Option: Answer is B**

Convert from base 5 to base 10

432five= (4 x 5^{2}) + (3 x 5^{1}) + (2 x 5^{0})

= (4 x 25) + (3 x 5) + (2 x 1)

= 100 + 15 + 2

= 117ten

Then convert from base 10 to base 3

3 | 117 |

3 | 39 r 0 |

3 | 13 r 0 |

3 | 4 r 1 |

3 | 1 r 1 |

| 0 r 1 |

Selecting the remainders from bottom to top:

117ten = 11100three

**3. **Given that A and B are sets such that n(A) = 8, n(B)=12 and n(AnB) =3, find n(AuB).

- A. 15
- B. 17
- C. 20
- D. 23

**Correct Option: Answer is B**

To find the cardinality of the union of sets A and B, denoted as n(A∪B), we can use the formula:

n(A∪B) = n(A) + n(B) – n(A∩B)

Given the information:

n(A) = 8 n(B) = 12 n(A∩B) = 3

We can substitute these values into the formula:

n(A∪B) = 8 + 12 – 3

n(A∪B) = 17

Therefore, the cardinality of the union of sets A and B, n(A∪B), is 17.

**4. **If √24 + √96 – √600 = y√6, find the value of y

- A. 4
- B. 2
- C. -2
- D. -4

**Correct Option: Answer is D**

To solve the equation √24 + √96 – √600 = y√6 and find the value of y, we can simplify the expression by simplifying each square root term.

√24 can be simplified as follows: √24 = √(4 × 6) = √4 × √6 = 2√6

Similarly, √96 can be simplified as: √96 = √(16 × 6) = √16 × √6 = 4√6

And √600 can be simplified as: √600 = √(100 × 6) = √100 × √6 = 10√6

Now we substitute these simplified values back into the original equation:

2√6 + 4√6 – 10√6 = y√6

(2 + 4 – 10)√6 = y√6

-4√6 = y√6

From this equation, we can see that the coefficient of √6 on both sides is -4. Therefore, we can determine that y is equal to -4.

Hence, the value of y is -4.

**5. **Evaluate 23 x 54 (mod 7)

- A. 2
- B. 3
- C. 5
- D. 6

**Correct Option: Answer is B**

To evaluate 23 x 54 (mod 7), we perform the multiplication first and then take the result modulo 7.

23 x 54 = 1242

Now, we find the remainder when 1242 is divided by 7 using the modulo operator:

1242 mod 7 = 3

Therefore, 23 x 54 (mod 7) is equal to 3.

**6. **If 4^{3x} = 16^{x+1}, find the value of x

- A. 2
- B. 3
- C. 4
- D. 5

**Correct Option: Answer is A**

4^{3x} = 16^{x+1}

4^{3x} = 4^{2(x+1)}

3x = 2x + 2

3x – 2x = 2; x = 2

**7. **A weaver bought a bundle of grass for $ 50.00 from which he made 8 mats. If each mat was sold for $ 15.00, find the percentage profit.

- A. 240%
- B. 140%
- C. 120%
- D. 40%

**Correct Option: Answer is B**

we need to determine the profit and then calculate it as a percentage of the cost price.

The cost price of the grass bundle is $50.00, and the weaver made 8 mats from it. Therefore, the cost price of each mat is:

Cost price per mat = Total cost / Number of mats = $50.00 / 8 = $6.25

The selling price of each mat is $15.00.

Now, let’s calculate the profit per mat:

Profit per mat = Selling price per mat – Cost price per mat = $15.00 – $6.25 = $8.75

To find the total profit, we multiply the profit per mat by the number of mats:

Total profit = Profit per mat * Number of mats = $8.75 * 8 = $70.00

Now, let’s calculate the percentage profit:

Percentage profit = (Total profit / Cost price) * 100% = ($70.00 / $50.00) * 100% = 140%

**8. **Find the 17term of the Arithmetic Progression (A.P):-6,-1,4

- A. -91
- B. -86
- C. 74
- D. 79

**Correct Option: Answer is C**

To find the 17th term of an arithmetic progression, you need to know the common difference (d) between consecutive terms. In this case, the first term (a₁) is -6, and the second term (a₂) is -1.

We can calculate the common difference (d) using the formula:

d = a₂ – a₁

Substituting the given values:

d = (-1) – (-6) = -1 + 6 = 5

Now, we can find the 17th term (a₁₇) using the formula for the nth term of an arithmetic progression:

aₙ = a₁ + (n – 1) * d

Substituting the values:

a₁₇ = -6 + (17 – 1) * 5 = -6 + 16 * 5 = -6 + 80 = 74

Therefore, the 17th term of the arithmetic progression -6, -1, 4 is 74.

**9. **M varies directly as n and inversely as the square of p. If M= 3 when n = 2 and p = 1, find M in terms of n and p.

- A. 3n/2p
^{2} - B. 2n/3p
^{2} - C. 2n/3p
- D. 3n
^{2}/p^{2}

**Correct Option: Answer is A**

To find the relationship between M, n, and p, we can write the direct and inverse proportionalities as follows:

M ∝ n M ∝ 1/p^2

Combining these proportionalities, we can express M in terms of n and p by introducing a constant of proportionality, k:

M = k * (n / p^2)

To find the value of k, we can use the given information that when n = 2 and p = 1, M = 3:

3 = k * (2 / 1^2) 3 = 2k k = 3/2

Now we can substitute the value of k back into our equation to find M in terms of n and p:

M = (3/2) * (n / p^{2})

M = (3/2) * (n / p^{2})

To simplify this expression, we can rewrite it as:

M = 3n / 2p^{2}

**10. **

** A. **0.51

- B. 0.91
- C. -0.19
- D. -0.51

**Correct Option: Answer is C**

**11. **Three boys shared D 10,500.00 in the ratio 6:7:8. Find the largest share.

- A. 4000
- B. 5000
- C. 4500
- D. 3500

**Correct Option: Answer is A**

To find the largest share, we need to determine the fraction of the total amount that each boy receives based on the given ratio. Let’s calculate:

The total ratio is 6 + 7 + 8 = 21.

To find the share for the first boy (with a ratio of 6), we calculate:

Share for the first boy = (6 / 21) * D10,500.00 = D3,000.00

For the second boy (with a ratio of 7), we calculate:

Share for the second boy = (7 / 21) * D10,500.00 = D3,500.00

For the third boy (with a ratio of 8), we calculate:

Share for the third boy = (8 / 21) * D10,500.00 = D4,000.00

Therefore, the largest share among the three boys is D4,000.00.

**12. **The length of a piece of stick is 1.75 m. A boy measured it as 1.80 m. Find the percentage error

- A. 4 4/7
- B. 2 6/7
- C. 2 7/9
- D. 4 7/9

**Correct Option: Answer is B**

To find the percentage error, we need to calculate the difference between the measured value and the actual value, and then express it as a percentage of the actual value. Let’s calculate:

Actual length of the stick = 1.75 m Measured length of the stick = 1.80 m

Difference = Measured length – Actual length Difference = 1.80 m – 1.75 m Difference = 0.05 m

Percentage error = (Difference / Actual length) * 100 Percentage error = (0.05 m / 1.75 m) * 100 Percentage error ≈ 2.857% == 2 6/7

**13. **If 5x + 3y=4 and 5x-3y= 2, what is the value of (25x^{2}-9y^{2})?

- A. 20
- B. 16
- C. 2
- D. 8

**Correct Option: Answer is D**

To find the value of (25x^{2} – 9y^{2}), we can use the given equations and solve for x and y. Let’s solve the system of equations:

Equation 1: 5x + 3y = 4 Equation 2: 5x – 3y = 2

Adding Equation 1 and Equation 2 eliminates the y term:

(5x + 3y) + (5x – 3y) = 4 + 2 10x = 6 x = 6/10 x = 3/5

Substituting the value of x into Equation 1 to solve for y:

5(3/5) + 3y = 4 3 + 3y = 4 3y = 4 – 3 3y = 1 y = 1/3

Now we have the values of x and y. Let’s substitute them into (25x^{2} – 9y^{2}):

(25(3/5)^{2}) – 9(1/3)^{2} (25(9/25)) – 9(1/9) 9 – 1 8

Therefore, the value of (25x^{2} – 9y^{2}) = 8.

**14. **Mary has $ 3.00 more than Ben but $ 5.00 less than Jane. If Mary has $ x, how much does Jane and Ben have altogether?

- A. $(2x-8)
- B. $(2x+8)
- C. $(2x-2)
- D. $(2x+2)

**Correct Option: Answer is D**

If Mary has $x, then Ben has $x-3 and Jane has $x+5. So, Jane and Ben have a total of $x-3+$x+5 = $2x+2

**15. **Consider the statements:

p: Stephen is intelligent

q: Stephen is good at Mathematics

If p⇒q, which of the following is a valid conclusion?

- A. If Stephen is good at Mathematics, then he is intelligent
- B. If Stephen is not good at Mathematics, then he is not intelligent
- C. If Stephen is not intelligent, then he is not good at Mathematics
- D. If Stephen is not good at Mathematics, then he is intelligent

**Correct Option: Answer is B**

If p implies (→) q

then not (~) q → not (~) p