∑ DANEMATHICS
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Grade 9 · Exponents
The Laws of Exponents: Complete Exam Guide
MARKING GUIDELINE
Marks
31
Duration
50 minutes
Questions
3
Name:
Class:
Date:
Mark
/ 31
Instructions and Information
- Answer ALL the questions in this question paper.
- Answer QUESTION 1 by circling the letter (A–D) in the answer grid at the end of that section.
- Show ALL calculations clearly.
- Show all units where applicable.
- Number the answers correctly according to the numbering system used in this question paper.
- A non-programmable calculator may be used, unless stated otherwise.
- Write neatly and legibly.
Question 1
[10 MARKS]Four options are given as possible answers to the following questions. Choose the correct answer and circle the letter (A–D) in the grid at the end of this section. If you want to change your choice, put a cross through the wrong letter and circle your new choice.
- 1.134 × 32 = …(1)A)38B)36✓C)96D)32Answer: B — Same base, multiplying: ADD the exponents.
- A — multiplied the exponents
- C — the BASE must not be multiplied too
- D — subtracted the exponents
- 1.2(2x3)4 = …(1)A)2x12B)16x12✓C)8x12D)16x7Answer: B — Everything inside is raised to the 4th: 24 = 16 and (x3)4 = x12.
- A — forgot to raise the 2
- C — used 23 instead of 24
- D — added the exponents instead of multiplying
- 1.315x73x2 = …(1)A)5x5✓B)12x5C)5x3,5D)5x9Answer: A — 15 ÷ 3 = 5 and x7 ÷ x2 = x5.
- B — SUBTRACTED the coefficients instead of dividing
- C — divided the exponents
- D — ADDED the exponents
- 1.4x0 + 20 = …(1)A)0B)2✓C)1D)3Answer: B — Each term is 1, and 1 + 1 = 2.
- A — a zero exponent gives 1, not 0
- C — only one of the two terms was counted
- D — there are only two terms
- 1.5Which one of the following is EQUAL to 23 × 42?(1)A)85B)27✓C)86D)26Answer: B — 42 = (22)2 = 24, so the product is 23+4.
- A — multiplied the bases as well
- C — multiplied the exponents
- D — used 42 = 23
- 1.6(a2b3)2 = …(1)A)a4b5B)a4b6✓C)a2b6D)2a2b3Answer: B — Multiply each exponent by 2.
- A — added 2 to the exponent of b instead of doubling it
- C — forgot to double the exponent of a
- D — multiplied the whole term by 2
- 1.75x3 + 5x3 = …(1)A)10x6B)10x3✓C)25x6D)5x6Answer: B — These are LIKE terms, so the exponent does not change.
- A — added the exponents as if multiplying
- C — multiplied the coefficients too
- D — forgot to add the coefficients
- 1.8x3 × x5x2 × x4 = …(1)A)x2✓B)x14C)x0D)x4Answer: A — Top: x8. Bottom: x6. So x8−6 = x2.
- B — added all four exponents
- C — the exponents do not cancel completely
- D — used 8 − 4, ignoring the x2 below
- 1.9If 2x = 32, then x = …(1)A)4B)5✓C)16D)6Answer: B — 25 = 32.
- A — 24 = 16
- C — halved 32
- D — 26 = 64
- 1.10(−3)2 × (−3)3 = …(1)A)(−3)6B)(−3)5✓C)35D)95Answer: B — Same base, so add the exponents: 2 + 3 = 5. (The value is −243.)
- A — multiplied the exponents
- C — the base is −3, not 3, and an odd power stays negative
- D — the base must not be squared as well
Answer grid — marking guideline
| 1.1 | A | B | C | D |
| 1.2 | A | B | C | D |
| 1.3 | A | B | C | D |
| 1.4 | A | B | C | D |
| 1.5 | A | B | C | D |
| 1.6 | A | B | C | D |
| 1.7 | A | B | C | D |
| 1.8 | A | B | C | D |
| 1.9 | A | B | C | D |
| 1.10 | A | B | C | D |
Question 2
[11 MARKS]Simplify the following. Leave your answers with positive exponents.
- 2.112a5b24a2b6(4)12 ÷ 4 = 3 (1)
a5−2 = a3 (1)
b2−6 = b−4 (1)
= 3a3b4 (1) - 2.2(2x2y3)3 × 3x−4(4)(2x2y3)3 = 8x6y9 (2)
× 3x−4 = 24x6−4y9 (1)
= 24x2y9 (1) - 2.3Calculate WITHOUT a calculator: (−32)(3)−2(3)−32 = −9 (the exponent applies to the 3 only) (1)
(3)−2 = 19 (1)
−9 × 19 = −1 (1)
Question 3
[10 MARKS]Answer the following WITHOUT using a calculator.
- 3.1Calculate: 42 − [6 ÷ (−2)]3(4)6 ÷ (−2) = −3 (1)
(−3)3 = −27 (1)
16 − (−27) (1)
= 43 (1) - 3.2Calculate: 12 × 70 + (5y)0(3)70 = 1, so 12 × 70 = 12 (1)
(5y)0 = 1 — the zero exponent applies to the WHOLE bracket, not just the y (1)
= 13 (1) - 3.3Show that 2−3 can be written as a common fraction, and give its value.(3)2−3 = 123 (1)
= 18 (2)
TOTAL: 31 marks
This question paper consists of 3 questions.