Algebraic expressions · Ages 13–14
Formulae & algebraic fractions worksheet
Covers: Simplifying algebraic fractions, Multiplying and dividing algebraic fractions, Adding and subtracting algebraic fractions, Substituting into formulae, Changing the subject of a formula, A new subject on both sides or below the line
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Formulae & algebraic fractions worksheet
Algebraic expressions · Ages 13–14
Numsprite
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Name:Date:Score:／48
Write each answer in the space. For word problems, show your working and write a sentence answer.
Part A: Working out and filling in (2 marks each)
1.Simplify: x2 + 17x + 72x + 9 = x +
Answer:
2.5x6 ÷ (2x27) = x (simplest form)
Fill in each blank
Answer:
3.3x + 95 ÷ x + 36 =
Answer in simplest form
Answer:
4.8x − 8 + 28 − x = x − 8
Answer:
5.2x + 1 + 1(x + 1)2 = x + (x + 1)2
Fill in each blank
Answer:
6.Celsius C to Fahrenheit F: F = 9C5 + 32. When C = −40, F =
Answer:
7.In the formula v = u + at, u = 11, a = 5 and t = 8: v =
Answer:
8.Make x the subject of y = 8x − 19: x = y +
Fill in each blank
Answer:
Part B: Choose, or true or false (2 marks each)
9.What is 6x + 67x2 + 7x in its simplest form?
- A. 6 + 67x + 7
- B. 67x
- C. 67
- D. 6x7
Choose the right answer
Answer:
10.Which is the formula S = 5(m − t) with t as its subject?
- A. t = S5 − m
- B. t = m − 5S
- C. t = m − S5
- D. t = m − S5
Choose the right answer
Answer:
11.From y = x + 19x − 1, it follows that x = y + 19y − 1.
True or false?
Answer:
12.Which is the formula y = 8x + kx − 3 with x as its subject?
- A. x = y + 38 + k
- B. x = y + 38k
- C. x = y + 3 − kx8
- D. x = y − 38 + k
Choose the right answer
Answer:
Part C: Word problems (4 marks each)
13.A cuboid's volume is (x3 + 11x2 + 24x) cm³; its base is (x + 8) cm by x cm. When x = 4, how tall is it, in cm?
Working:
Answer:
14.A rectangle is 2xx + 5 cm long and x + 53 cm wide. Area = 2xx + 5 × x + 53 = x cm² (simplest form).
Fill in each blank
Working:
Answer:
15.Put the steps of working out 6x − 2 − 2x + 2 in order.
- A. 6x + 12 − 2x + 4x2 − 4 = 4x + 16x2 − 4
- B. 6x − 2 − 2x + 2 = 6(x + 2) − 2(x − 2)x2 − 4
- C. 6(x + 2) − 2(x − 2)x2 − 4 = 6x + 12 − 2x + 4x2 − 4
Write the letters in the right order
Working:
Answer:
16.Hiring a camper van costs C = 120 + 180n, C in dollars and n the number of days. A family paid $1,380. For how many days?
Working:
Answer:
17.A city's taxi fare is about C = 27 + 9d, C in dollars and d the distance in km. With d as the subject: d = C − ; a $171 fare means about km.
Fill in each blank
Working:
Answer:
18.Put the steps of making x the subject of y = x + 18x − 9 in order.
- A. y(x − 9) = x + 18
- B. x(y − 1) = 9y + 18
- C. xy − x = 9y + 18
- D. x = 9y + 18y − 1
Write the letters in the right order
Working:
Answer:
Show the answers and working
Formulae & algebraic fractions worksheet: Answers and working
Part A: Working out and filling in
1. 8
9 × 8 = 72 and 9 + 8 = 17, so x2 + 17x + 72 = (x + 9)(x + 8). Cancel x + 9: x + 8.
2. 35, 12
Dividing by 2x27 is multiplying by 72x2: 5x × 76 × 2x2 = 3512x = 3512x.
3. 185
Dividing by x + 36 is multiplying by 6x + 3: 3x + 35 × 6x + 3; x + 3 cancels, leaving 3 × 65 = 185.
4. 6
8 − x = −(x − 8), so 28 − x = −2x − 8: the top is 8 − 2 = 6.
5. 2, 3
The common denominator is (x + 1)2, not (x + 1)3: the top is 2(x + 1) + 1 = 2x + 3.
6. −40
F = 9 × (−40) ÷ 5 + 32 = −40. A negative value goes in a bracket.
7. 51
v = 11 + 5 × 8 = 51. Times before plus.
8. 19, 8
Add 19 to both sides: y + 19 = 8x; divide both by 8: x = y + 198.
Part B: Choose, or true or false
9. B. 67x
Top = 6(x + 1), bottom = 7x(x + 1); cancel x + 1: 67x.
10. C. t = m − S5
Divide both sides by 5: S5 = m − t; then move the terms: t = m − S5.
11. True
y(x − 1) = x + 19, xy − x = y + 19, x(y − 1) = y + 19, x = y + 19y − 1.
12. A. x = y + 38 + k
y + 3 = 8x + kx = x(8 + k), so x = y + 38 + k.
Part C: Word problems
Marking: 2 for the working, 1 for the answer, 1 for the sentence.
13. 7 cm
x3 + 11x2 + 24x = x(x + 8)(x + 3); divided by the base area x(x + 8), the height is x + 3 = 7 cm.
14. 2, 3
x + 5 cancels above and below: 2x3 = 2x3.
15. B → C → A
Bring them over the common denominator (x − 2)(x + 2) = x2 − 4; open the top, every term of −2(x − 2) changing sign; then collect like terms.
16. 7 days
Substitute: 1380 = 120 + 180n, so 180n = 1380 − 120 and n = 7.
17. 27, 9, 16
Take 27 from both sides, then divide by 9: d = C − 279; with C = 171, d = 171 − 279 = 16.
18. A → C → B → D
Clear the denominator, open the bracket, gather the x terms on one side, take x out as a factor, then divide by y − 1.
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