Algebraic Expressions and Properties of Real Numbers: math test solutions, Grade 9 – download the PDF

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Test solutions with the detailed point scale. Add up your points and spot what to review.

Suggested time: 45 minutes. Out of 20 points. Calculator allowed only when the problem says so.

Sommaire

a) $9-4=5$, $5^2=25$, $2\cdot 25=50$, $50\div 5=10$, then $7+10=17$. (2 pts)

b) $2(-3)^2-3(-3)(4)+4=2(9)+36+4=18+36+4=58$. (2 pts)

a) Additive inverse property. (1 pt)

b) Associative property of multiplication. (1 pt)

c) Distributive property. (1 pt)

a) $p$ terms: $8+2-1=9$, constants: $-3+11=8$. The result is $9p+8$. (2 pts)

b) $10y+5-3y+12=7y+17$. (2 pts)

a) $\sqrt{36}=6$: natural, whole, integer, and rational. (1 pt)

b) $-4.5=-\dfrac{9}{2}$: rational only. (1 pt)

c) $30$ is not a perfect square: irrational only. (1 pt)

a) $\dfrac{n}{5}+3$. (1 pt)

b) $2(n-8)$. The parentheses are needed because the 2 multiplies the whole difference. (1 pt)

c) $4+2.5m$; for $m=8$: $4+20=24$, so the ride costs $24. (1 pt)

a) $P=2(2x+3)+2x=4x+6+2x=6x+6$. (1 pt)

b) $A=x(2x+3)=2x^2+3x$. (1 pt)

c) For $x=5$: $P=6(5)+6=36$ ft and $A=2(25)+15=65$ square feet. Check: length 13 ft, width 5 ft, so $2(13)+2(5)=36$ and $13\cdot 5=65$. (1 pt)

Test yourself: quick challenge for Grade 9