Practice Test - Solving Equations PDF

**PRACTICE TEST: Solving Equations** **See if you can complete it in 70 minutes** **SCORE:** **Out of 65** +-----------------------------------+-----------------------------------+ | **PART 1 - MULTIPLE CHOICE -- | | | SELECT ONE ANSWER ONLY -- USE A |...

**PRACTICE TEST: Solving Equations** **See if you can complete it in 70 minutes** **SCORE:** **Out of 65** +-----------------------------------+-----------------------------------+ | **PART 1 - MULTIPLE CHOICE -- | | | SELECT ONE ANSWER ONLY -- USE A | | | PENCIL** | | +===================================+===================================+ | 1. Select the solution to | 2. Select a solution to | | [20 − *c* = 3*c* + 4]{.math | [*y* = *y*^2^ − 4*y*]{.math | |.inline}. |.inline}. | | | | | | | | | | | A. [*c* = 0]{.math.inline} | A. [*y* =  − 1]{.math.inline} | | | | | B. [*c* = 1]{.math.inline} | B. [*y* = 0]{.math.inline} | | | | | C. [*c* = 2]{.math.inline} | C. [*y* = 1]{.math.inline} | | | | | D. [*c* = 3]{.math.inline} | D. [*y* = 2]{.math.inline} | | | | | E. [*c* = 4]{.math.inline} | E. [*y* = 3]{.math.inline} | +-----------------------------------+-----------------------------------+ | 3. Select the best first step to | 4. Select the linear equation | | solve: | that represents the sentence | | | "the answer is thirteen when | | \ | four is subtracted from | | [8 + 2*x* = 32]{.math.display}\ | double a certain number". | | | | | A. Subtract 32 from the right | | | side. | | | | A. [13 + 2*n* =  − 4]{.math | | B. Divide the left side by |.inline} | | {.math.inline}. | | | | B. [ − 4*n* × 2 = 13]{.math | | C. Subtract 8 from the left side |.inline} | | only. | | | | C. [13 − 4 = 2*n*]{.math | | D. Subtract 8 from both sides. |.inline} | | | | | E. Divide the right side by | D. [13 = 4 − *n*]{.math.inline} | | {.math.inline}. | | | | E. [2*n* − 4 = 13]{.math | | |.inline} | +-----------------------------------+-----------------------------------+ | 5. Select the equation that | 6. Rearrange the following | | represents the completed | equation to make [*c*]{.math | | first step when solving: |.inline} the subject: | | | | | \ | \ | | [1 = 4*r* − 11]{.math.display}\ | [2*a* = 4*b* − *c*]{.math | | |.display}\ | | A. [1 =  − 7*r*]{.math.inline} | | | | A. [*c* =  − 2*a* − 4*b*]{.math | | B. [3*r* =  − 11]{.math.inline} |.inline} | | | | | C. [ − 7*r* =  − 1]{.math | B. [*c* =  − 2*a* + 4*b*]{.math | |.inline} |.inline} | | | | | D. [ − 4*r* =  − 10]{.math | C. [*c* = 4*a* − 2*b*]{.math | |.inline} |.inline} | | | | | E. [4*r* = 12]{.math.inline} | D. [*c* =  − 4*a* + 2*b*]{.math | | |.inline} | | | | | | E. [*c* = 6ab]{.math.inline} | +-----------------------------------+-----------------------------------+ | 7. Select the best first step to | 8. Select the best first step to | | solve: | solve: | | | | | \ | \ | | [8(*h*−37) = 24]{.math.display}\ | [5(*g*−7) = 32]{.math.display}\ | | | | | A. Divide both sides by | A. Divide both sides by | | {.math.inline}. | {.math.inline}. | | | | | B. Add {.math.inline} to | B. Add {.math.inline} to | | both sides. | both sides. | | | | | C. Subtract {.math.inline} | C. Subtract {.math.inline} | | from both sides. | from both sides. | | | | | D. Expand the brackets. | D. Expand the brackets. | | | | | E. Subtract [*h*]{.math.inline} | E. Subtract [*g*]{.math.inline} | | from both sides. | from both sides. | +-----------------------------------+-----------------------------------+ | 9. If you add 2 to one side of | 10. The inverse operation of | | an equation... | addition is: | | | | | | | | | | | A.... add 2 to the other side | A. Multiplication | | as well. | | | | B. Division | | B.... subtract 2 from the other | | | side. | C. Indices | | | | | C.... do nothing to the other | D. Addition | | side. | | | | E. Subtraction | | D.... divide the other side | | | by 2. | | | | | | E.... add 3 to the other side. | | +-----------------------------------+-----------------------------------+ +-----------------------------------+-----------------------------------+ | **PART 2 -- SHORT ANSWER -- | | | ALWAYS SHOW WORKING OUT -- USE A | | | PENCIL** | | +===================================+===================================+ | 1. Solve [35.7 + *w* = 50]{.math | 2. Solve [\$\\frac{m}{7} = | |.inline} | 3\$]{.math.inline} | | | | | **\ | **/2** | | ** | | | | | | ***Did you show working out? | | | These are worth two marks.* /2** | | +-----------------------------------+-----------------------------------+ | 3. Solve [15 = 3*y*]{.math | 4. Solve [*n* − 14 = 6]{.math | |.inline} |.inline} | | | | | **\ | **/2** | | ** | | | | | | **/2** | | +-----------------------------------+-----------------------------------+ | 5. Using substitution, show that | 6. Using substitution, show that | | [*p* = 3]{.math.inline} is | [*u* = 4]{.math.inline} is a | | not a solution to the | solution to the following | | following equation: | equation: | | | | | \ | \ | | [3*p* − 1 = 1 + 2*p*]{.math | [3*u* + 2 = *u*^2^ − 2]{.math | |.display}\ |.display}\ | | | | | **/2** | **\ | | | ** | | | | | | **/2** | +-----------------------------------+-----------------------------------+ | 7. Solve [30*t* − 2 = 38]{.math | 8. Solve [\$\\frac{r}{100} - 18 | |.inline} | = 7\$]{.math.inline} | | | | | **\ | **/2** | | ** | | | | | | **/2** | | +-----------------------------------+-----------------------------------+ | 9. Solve [7 − 5*y* = 12]{.math | 10. Solve [\$\\frac{x - 3}{4} = | |.inline} | 2\$]{.math.inline} | | | | | **\ | **/2** | | ** | | | | | | **/2** | | +-----------------------------------+-----------------------------------+ | 11. Solve [3(*d* − 7) = 25]{.math | 12. Solve [33(*q*+14) = 99]{.math | |.inline} |.inline} | | | | | **\ | **/2** | | ** | | | | | | **/2** | | +-----------------------------------+-----------------------------------+ | 13. Solve [5*z* − 1 = *z*]{.math | 14. Solve [3*x* + 1 =  − 5]{.math | |.inline} |.inline} | | | | | **\ | **/2** | | ** | | | | | | **/2** | | +-----------------------------------+-----------------------------------+ | 15. Solve | 16. Solve | | [7*s* + 3 = 13 − 3*s*]{.math | [4 − *m* = 2*m* − 5]{.math | |.inline} |.inline} | | | | | **/2** | **\ | | | ** | | | | | | **/2** | +-----------------------------------+-----------------------------------+ | 17. Solve | 18. Solve | | [6*b* − 4 = 2(*b*+4)]{.math | [10(*k* − 1) = 5(4 − *k*)]{.m | |.inline} | ath | | |.inline} | | **\ | | | ** | **/2** | | | | | **/2** | | +-----------------------------------+-----------------------------------+ | 19. Write an equation for the | 20. Write an equation for the | | following statement then | following statement then | | solve it: *"When eleven is | solve it: *"A certain number | | subtracted from a certain | is divided by three, then one | | number, the result is | is added, the answer is | | forty-six."* | ten."* | | | | | **\ | **/2** | | ** | | | | | | **/2** | | +-----------------------------------+-----------------------------------+ | 21. Make [*h*]{.math.inline} the | 22. Rearrange to make [*x*]{.math | | subject: |.inline} the subject: | | [5 + *h* = *g*^2^ + 1]{.math | [*y* = 4*x* + 12]{.math | |.inline} |.inline} | | | | | **\ | **/2** | | ** | | | | | | **/2** | | +-----------------------------------+-----------------------------------+ | 23. Make [*p*]{.math.inline} the | 24. Rearrange to make [*q*]{.math | | subject: |.inline} the subject: [\$f = | | [9 + 3*w* = 3(*p* + 1)]{.math | \\frac{3v}{1 + q}\$]{.math | |.inline} |.inline} | | | | | **\ | **/2** | | ** | | | | | | **/2** | | +-----------------------------------+-----------------------------------+ | 25. Mary wants to go on a trip to | | | Europe. It costs her \$5000 | | | for the flights and then | | | another \$250 for each night | | | that she spends there. | | | | | | a. Write an equation where | | | [*C*]{.math.inline} | | | represents the total cost | | | for Mary and [*n*]{.math | | |.inline} represents the | | | number of nights she | | | spends in Europe. | | | | | | b. If she wants to spend 15 | | | nights in Europe, how | | | much does she need to | | | save up? | | | | | | c. If she has \$15,000 in | | | the bank, then how many | | | nights can she stay in | | | Europe for? | | | | | | **\ | | | ** | | | | | | **/3** | | +-----------------------------------+-----------------------------------+ | 26. Rosehill Primary School is | | | building a miniature | | | basketball court for little | | | preppies. Its length is 4 | | | metres greater than its | | | width. What is its length if | | | the total perimeter is 20 | | | metres? | | | | | | **/2** | | +-----------------------------------+-----------------------------------+ | 27. Adult tickets for Puffing | | | Billy cost \$62, a child | | | ticket costs \$31. If a large | | | group spent \$620 and there | | | were twice as many adults as | | | there were children, then how | | | many adults were in the | | | group? | | | | | | **/2** | | +-----------------------------------+-----------------------------------+