Practice:  Pre Algebra (1.3 – 1.6) — Intermediate Algebra

35 Practice: Pre Algebra (1.3 – 1.6) — Intermediate Algebra

Answer keys are in section that follows.

For questions 1 to 24, reduce and solve the following expressions.

$-6 \cdot 4(-1)$
$(-6 \div 6)^3$
$3 + (8) \div | 4 |$
$5(-5 + 6) \cdot 6^2$
$8 \div 4 \cdot 2$
$7 - 5 + 6$
$[-9 - (2 - 5)] \div (-6)$
$(-2 \cdot 2^3 \cdot 2) \div (-4)$
$-6 + (-3 - 3)^2 \div | 3 |$
$(-7 - 5) \div [-2 - 2 - (-6)]$
$4 - 2 | 3^2 - 16 |$
$(-10 - 6) \div (-2)^2 - 5$
$[ -1 - (-5)] | 3 + 2 |$
$-3 - \{3 - [ -3(2 + 4) - (-2)]\}$
$[2 + 4 |7 + 2^2|] \div [4 \cdot 2 + 5 \cdot 3]$
$-4 - [2 + 4(-6) - 4 - 22 - 5 \cdot 2]$
$[6 \cdot 2 + 2 - (-6)] (-5 + | (-18 \div 6) |)$
$2 \cdot (-3) + 3 - 6[ -2 - (-1 - 3)]$
$\dfrac{-13-2}{2-(-1)^3+(-6)-[-1-(-3)]}$
$\dfrac{5^2+(-5)^2}{| 4^2-2^5| -2 \cdot 3}$
$\dfrac{6 \cdot -8 - 4 + (-4) - [ -4 -(-3)]}{(4^2 + 3^2) \div 5}$
$\dfrac{-9 \cdot 2 - (3 - 6)}{1-(-2+1)-(-3)}$
$\dfrac{2^3 + 4}{-18 - 6 + (-4) - [ -5(-1)(-5)]}$
$\dfrac{13 + (-3)^2 + 4(-3) + 1 - [ -10 - (-6)]}{\{[4 + 5] \div [4^2 - 3^2(4 - 3) - 8]\} + 12}$

For questions 1 to 28, reduce and combine like terms.

For questions 29 to 58, simplify each expression.

$9(b + 10) + 5b$
$4v - 7(1 - 8v)$
$-3x(1 - 4x) - 4x^2$
$-8x + 9(-9x + 9)$
$-4k^2 - 8k(8k + 1)$
$-9 - 10(1 + 9a)$
$1 - 7(5 + 7p)$
$-10(x - 2) - 3$
$-10 - 4(n - 5)$
$-6(5 - m) + 3m$
$4(x + 7) + 8(x + 4)$
$-2r(1 + 4r) + 8r(-r + 4)$
$-8(n + 6) - 8n(n + 8)$
$9(6b + 5) - 4b(b + 3)$
$7(7 + 3v) + 10(3 - 10v)$
$-7(4x - 6) + 2(10x - 10)$
$2n(- 10n + 5) - 7(6 - 10n)$
$-3(4 + a) + 6a(9a + 10)$
$5(1 - 6k) + 10(k - 8)$
$-7(4x + 3) - 10(10x + 10)$
$(8n^2 - 3n) - (5 + 4n^2)$
$(7x^2 - 3) - (5x^2 + 6x)$
$(5p - 6) + (1 - p)$
$(3x^2 - x) - (7 - 8x)$
$(2 - 4v^2) + (3v^2 + 2v)$
$(2b - 8) + (b - 7b^2)$
$(4 - 2k^2) + (8 - 2k^2)$
$(7a^2 + 7a) - (6a^2 + 4a)$
$(x^2 - 8) + (2x^2 - 7)$
$(3 - 7n^2) + (6n^2 + 3)$

For questions 1 to 18, use dimensional analysis to perform the indicated conversions.

For questions 19 to 27, solve each conversion word problem.

On a recent trip, Jan travelled 260 miles using 8 gallons of gas. What was the car’s miles per gallon for this trip? Kilometres per litre?
A certain laser printer can print 12 pages per minute. Determine this printer’s output in pages per day.
An average human heart beats 60 times per minute. If the average person lives to the age of 86, how many times does the average heart beat in a lifetime?
Blood sugar levels are measured in milligrams of glucose per decilitre of blood volume. If a person’s blood sugar level measured 128 mg/dL, what is this in grams per litre?
You are buying carpet to cover a room that measures 38 ft by 40 ft. The carpet cost $18 per square yard. How much will the carpet cost?
A cargo container is 50 ft long, 10 ft wide, and 8 ft tall. Find its volume in cubic yards and cubic metres.
A local zoning ordinance says that a house’s “footprint” (area of its ground floor) cannot occupy more than ¼ of the lot it is built on. Suppose you own a $\frac{1}{3}$ -acre lot (1 acre = 43,560 ft²). What is the maximum allowed footprint for your house in square feet? In square metres?
A car travels 23 km in 15 minutes. How fast is it going in kilometres per hour? In metres per second?
The largest single rough diamond ever found, the Cullinan Diamond, weighed 3106 carats. One carat is equivalent to the mass of 0.20 grams. What is the mass of this diamond in milligrams? Weight in pounds?

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