Oakland Math TestSelect Questions and Answers

NOT Multiple Choice

What number added to the sum of equal the number 1?

𝑥+ 13 +14=1

12𝑥+4+3=12

12𝑥=5

𝑥= 512

(43 )2

16=?

(43 )2

16=4

6

42=44=254

solve for w.

10𝑤=35𝑤=3.5

Jan is making clay coasters for an art fair. Each coaster costs $2.25 to make. If she sells the coasters for $4.00 each, how many will she have to sell to make a profit of exactly $70.00?

𝐿𝑒𝑡 𝑥𝑏𝑒 h𝑡 𝑒𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑐𝑜𝑎𝑠𝑡𝑒𝑟𝑠 h𝑠 𝑒𝑚𝑎𝑘𝑒 .𝑝𝑟𝑜𝑓𝑖𝑡 𝑜𝑓 h𝑒𝑎𝑐 × h𝑡 𝑒𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑐𝑜𝑎𝑠𝑡𝑒𝑟𝑠=𝑝𝑟𝑜𝑓𝑖𝑡

(4.00−2.25 ) 𝑥=70.00

1.75 𝑥=70𝑥=40

Four pieces of ribbon are cut from a length of ribbon that is 80 ft long. One of the pieces is 15 feet long. Two of the pieces are 7½ feet long. One of the pieces is 3¾ feet long. How many feet of ribbon are left from the original length?

𝐿𝑒𝑡 𝑥 𝑓𝑡 𝑏𝑒 h𝑡 𝑒 h𝑙𝑒𝑛𝑔𝑡 𝑜𝑓 h𝑡 𝑒 𝑙𝑒𝑓𝑡𝑜𝑣𝑒𝑟 𝑝𝑖𝑒𝑐𝑒 .15+2(7 12 )+3 34 +𝑥=80

15+15+ 154 +𝑥=80154 +𝑥=50

15+4 𝑥=2004 𝑥=185𝑥=46 14 𝑓𝑡

A taxi cab charges $0.80 for the first of a mile and $0.10 for each additional of a mile. What is the cost of 3 mile trip?

𝐿𝑒𝑡 $ 𝑥𝑏𝑒 h𝑡 𝑒𝑐𝑜𝑠𝑡

𝑥=0.80+0.10 [ (3− 15 )110

]𝑥=𝑐𝑜𝑠𝑡 𝑜𝑓 1 𝑠𝑡 15𝑚𝑖𝑙𝑒+𝑐𝑜𝑠𝑡 𝑜𝑓 h𝑡 𝑒𝑟𝑒𝑠𝑡𝑜𝑓 h𝑡 𝑒𝑡𝑟𝑖𝑝

𝑥=0.80+0.10 [ 145110

]𝑥=0.80+0.10 (28)𝑥=0.80+2.80𝑥=3.60

Another Method: since taxi cab charges by tenths of a mile. For a 3 mile trip, there are 30 tenths of a mile. The first or 2 tenths of a mile costs 80¢, the rest, 28 tenths of a mile costs 10¢.

𝑐𝑜𝑠𝑡=80¢+10¢(28)

Continue

¿80+280=360=$3.60

John works a variety of different jobs. On Monday he earned $50. Tuesday he earned $40. On Wednesday and Thursday he earned $30 each day, and ion Friday he earned $100. What was john’s average daily pay for the 5 days?

𝐴𝑣𝑒𝑟𝑎𝑔𝑒=50+40+30+30+100

5

¿2505 =$50

Evaluate:

3 (−2 )2−2 (−2 ) (3 )+32

¿3 (4 )+12+9

¿12+12+9

¿33

Simplify:

(𝑥+ 𝑦 )2− (9𝑥𝑦−6 𝑥2 )¿ 𝑥2+2𝑥𝑦+ 𝑦2−9 𝑥𝑦+6 𝑥2

¿7 𝑥2−7𝑥𝑦+ 𝑦2

Multiply:

(2 𝑥−5 ) (6 𝑥+4 )

¿12 𝑥2+8𝑥−30 𝑥−20

¿12 𝑥2−22 𝑥−20

Divide:

12𝑥5−6 𝑥3+4 𝑥2

4 𝑥2

¿12𝑥5

4 𝑥2− 6 𝑥

3

4 𝑥2+4 𝑥2

4 𝑥2

¿3 𝑥3− 32 𝑥+1

Factor:

6 𝑥3+27 𝑥2−105 𝑥¿3 𝑥 (2𝑥2+9 𝑥−35)

¿3 𝑥 (2 𝑥−5 ) (𝑥+7 )

Simplify:

𝑥2−5 𝑥+4𝑥−1

¿(𝑥−4 ) (𝑥−1 )

𝑥−1

¿ 𝑥−4

Simplify:

¿3+4=7

Evaluate: , find A

𝐴=𝑃 (1+𝑟 )

𝐴=450 (1+0.12 )

𝐴=450(1.12)

𝐴=504

Simplify:

√18 𝑥−4√𝑥3¿3 √2 𝑥−4 𝑥 √𝑥

Rationalize:

2+√32−√3

∙(2+√3 )(2+√3 )

¿ 4+4√3+34−3

¿7+4 √3

Solve:

3 𝑥+7=2(𝑥−1)

3 𝑥+7=2𝑥−2

𝑥+7=−2𝑥=−9

Find the sum of the roots:

𝑥2−6 𝑥=7𝑥2−6 𝑥−7=0

(𝑥+1 ) (𝑥−7 )=0

𝑥+1=0 𝑜𝑟 𝑥−7=0

𝑥=−1𝑜𝑟 𝑥=7

𝑠𝑢𝑚𝑜𝑓 𝑟𝑜𝑜𝑡𝑠=−1+7=6

Solve for x:

1𝑥 +

2𝑥=10

1+2=10 𝑥

10 𝑥=3

𝑥= 310

Solve the Inequality:

−2 𝑥+3<5−2 𝑥<2𝑥>−1

System of Equations:

(1 )2𝑥+3 𝑦=−11(2 )6 𝑥+𝑦=7

𝐹𝑟𝑜𝑚 (2): 𝑦=7−6 𝑥𝑆𝑢𝑏 𝑡𝑜 (1 ) :2 𝑥+3 (7−6 𝑥 )=−11

2 𝑥+21−18 𝑥=−11−16 𝑥=−32𝑥=2

𝑦=7−6 (2 )=7−14=−7

Solution:

Simplify the Expression:

2𝑎− 2

(2𝑎)− 3

¿2 (2𝑎)3

𝑎2

¿2 (8𝑎3 )𝑎2

¿16𝑎3

𝑎2

¿16 𝑎

Scientific Notation:

(2.1×105 )2

¿ (2.1×105 ) (2.1×105 )

¿ 4.41×1010

Radicals:

3√𝑎 ∙ 4√𝑎¿𝑎1 /3 ∙𝑎1 /4

¿𝑎13 +14

¿𝑎412+ 312

¿𝑎712

¿ 12√𝑎7

Altogether Mark, John, and Alan earned $104. John earned twice as much as Mark and Alan earned $4 more than John. How much did Alan earn?

𝐿𝑒𝑡 $ 𝑥𝑏𝑒 h𝑡 𝑒𝑎𝑚𝑜𝑢𝑛𝑡 𝑀𝑎𝑟𝑘𝑒𝑎𝑟𝑛𝑒𝑑h𝐽𝑜 𝑛=2 𝑥

𝐴𝑙𝑎𝑛= h𝐽𝑜 𝑛+4=2𝑥+4

𝑀𝑎𝑟𝑘+ h𝐽𝑜 𝑛+ 𝐴𝑙𝑎𝑛=104𝑥+2𝑥+2𝑥+4=104

5 𝑥+4=1045 𝑥=100𝑥=20

𝑀𝑎𝑟𝑘=$20

h𝐽𝑜 𝑛=2 (20 )=$ 40

𝐴𝑙𝑎𝑛=2 (20 )+4=$ 44

A train travels 4 hrs at 60 miles per hour and 2 hours at 75 miles per hour. What is the train’s average rate for 6 hours?

𝐴𝑣𝑒𝑟𝑎𝑔𝑒=𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒𝑜𝑓 1 𝑠𝑡𝑝𝑎𝑟𝑡+𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒𝑜𝑓 2𝑛𝑑𝑝𝑎𝑟𝑡

𝑇𝑜𝑡𝑎𝑙𝑡𝑖𝑚𝑒

𝐴𝑣𝑒𝑟𝑎𝑔𝑒=4 (60 )+2 (75 )

6

¿3906 =65 h𝑚𝑝

Graph:

2 𝑥+𝑦=5𝑦=−2𝑥+5

𝑚=−21 𝑜𝑟

2−1 𝑎𝑛𝑑𝑏=5

Start with point A, where b = 5 or (0, 5).For point B, start from point A, go down 2 and go to the right 1, For point C, start from point A,go up 2 and go to the left 1.

𝐴

𝐵

𝐶

Slope: Are these two lines parallel?

𝐿13 𝑦=−2𝑥+6

𝑦=− 23 𝑥+2 ;𝑚1=−23

𝐿2𝑚2=7−105−3 =

−32

𝐿1𝑎𝑛𝑑𝐿2𝑎𝑟𝑒𝑁𝑂𝑇 𝑝𝑎𝑟𝑎𝑙𝑙𝑒𝑙 ,𝑠𝑙𝑜𝑝𝑒𝑠𝑎𝑟𝑒 𝑁𝑂𝑇 𝑒𝑞𝑢𝑎𝑙 .

Write the equation of the line through (2, -1) and has slope m = 3. Write the equation in general form (standard form).

(2 ,−1 )𝑥1 , 𝑦1

𝑦− 𝑦1=𝑚 (𝑥−𝑥1 )

𝑦− (−1 )=3(𝑥−2)

𝑚=3

𝑦+1=3 𝑥−6−3 𝑥+𝑦=−7

Standard form

What is the distance between A(2, -5) and B(6, 3)? (Round to the nearest tenth).

𝐴 (2 ,−5 )𝐵 (6 ,3)𝑥1 𝑦1𝑥2 𝑦2

𝐷=√𝑟𝑖𝑠𝑒2+𝑟𝑢𝑛2

𝐷=√ ( 𝑦2− 𝑦1 )2+ (𝑥2−𝑥1)2

𝐷=√ (3+5 )2+(6−2 )2

𝐷=√ (8 )2+ (4 )2

𝐷=√64+16𝐷=√80𝐷=4√5

Graph:

𝑦=−𝑥2+4𝑦=−(𝑥2−4)𝑦=− (𝑥+2 ) (𝑥−2 )𝑟𝑜𝑜𝑡𝑠 : 𝐴 (−2 ,0 ) ,𝐵 (2 ,0 )

𝑎𝑥𝑖𝑠𝑜𝑓 𝑠𝑦𝑚𝑚𝑒𝑡𝑟𝑦 :𝑥=− 𝑏2𝑎

𝑥=− 02 (−1 )

=0

𝑎=−1 ;𝑏=0 ;𝑐=4

𝑦=−02+4=4𝑀𝑎𝑥=𝐶(0 ,4 )

𝐴𝐵

𝐶

.

¿𝑎2+2𝑎+1+2𝑎+2+3

¿𝑎2+4𝑎+6

What is the domain of ?

2 𝑥+6=02 𝑥=−6𝑥=−3

The domain of f(x) is ALL real numbers except -3

𝐷𝑜𝑚𝑎𝑖𝑛=(−∞ ,−3 )∪ (−3 ,∞ )

h𝑊 𝑒𝑛𝑖𝑠 𝑓 (𝑥 )𝑢𝑛𝑑𝑒𝑓𝑖𝑛𝑒𝑑?

What is the domain of

𝑥−7 ≥0𝑥≥7h𝑇 𝑒𝑑𝑜𝑚𝑎𝑖𝑛𝑜𝑓 𝑓 (𝑥 ) 𝐴𝑙𝑙𝑟𝑒𝑎𝑙 𝑁𝑢𝑚𝑏𝑒𝑟𝑠≥7

𝑑𝑜𝑚𝑎𝑖𝑛=¿

Composition of functions: Find

( 𝑓 ∙𝑔) (3 )= 𝑓 (3) ∙𝑔(3)¿ [3 (3 )−2 ] ∙[32+1]

¿7 ∙10( 𝑓 ∙𝑔 ) (3 )=70

Composition of functions: Find .

𝑓 (𝑔 (3 ) )= 𝑓 (32+1)¿ 𝑓 (10)¿3 (10 )−2

𝑓 (𝑔 (3 ))=28

𝑓 (𝑔 (3 ) )=( 𝑓 ∘𝑔)(3)