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1. In a group of cows and chickens, the number of legs was 14 more than twice the number of heads. The number of cows was:
(a) 5, (b) 7, (c) 10, (d) 12, (e) 14
Let the number of cows be x and their legs be 4x.
Let the number of chicken be y and their legs be 2x.
Total number of legs = 4x + 2y.
Total number of heads = x + y.
The number of legs was 14 more than twice the number of heads.
Therefore, 2 × (x + y) + 14 = 4x + 2y.
or, 2x + 2y + 14 = 4x + 2y.
or, 2x + 14 = 4x [subtracting 2y from both sides].
or, 14 = 4x – 2x [subtracting 2x from both sides].
or, 14 = 2x.
or, x = 7 [dividing by 2 on both sides].
Therefore, the number of cows = 7.
2. The roots of the equation ax2 + bx + c = 0 will be reciprocal if:
4. A circle of radius 10 inches has its center at the vertex C of an
equilateral triangle ABC and passes through the other two vertices. The
side AC extended through C intersects the circle at D. The number of
degrees of angle ADB is:
(a) 15, (b) 30, (c) 60, (d) 90, (e) 120
8. A 7-in. pizza costs $8 and a 14-in. pizza costs $20. Tommy says
the smaller pizza is a better buy because the larger pizza is twice as
big and more than twice as expensive. Do you agree with his reasoning?
If not, explain why not.
No, a pizza looks like a circle.
And we know that area of a circle depends on the radius.
So, we can clearly say that area of a circle is proportional to the square of the diameter.
Similarly, the cost a pizza depends on its area not its diameter.
9. Suppose that Jody drove 80 miles in 2 hours. Dividing 80 by 2
tells us how many miles Jody drove in each hour. The units for this rate
are miles per hour (mi/hr). If we divide 2 by 80 what information would
this give us? Give an interpretation of the rate. What units would be
used for this rate?
We know that, speed = distance/time.
When total distance is divided by total time we get the speed.
Here, speed = distance covered in 1 hour.
According to the question,
Total distance 80 miles divided by total time 2 hours = 80/2.
miles/hour = 40 mile/hour.
Therefore, Jody drove 40 miles in 1 hour.
But if we divide total time by total distance then, we get time taken to cover 1 mile.
Similarly, if we divide 2 by 80 then, we get time taken to cover 1 mile.
Therefore, unit used for this case = hours/mile.
10. 19/6 = 4/27. Which method did you use to determine whether this proportion is true or false?
19/6 = 4/27.
19 × 27 = 513.
6 × 4 = 24.
We see that 513 are not equal to 24.
Therefore, we determine 19/6 = 4/27 is not proportion so, the answer is false.
On Thursday Mabel handled 90 transactions. Anthony handled 10% more
transactions than Mabel, Cal handled 2/3rds of the transactions that
Anthony handled, and Jade handled 16 more transactions than Cal. How
much transactions did Jade handled?
Mabel handled 90 transactions
Anthony handled 10% more transactions than Mabel
Anthony = 90 + 90 × 10%
= 90 + 90 × 0.10
= 90 + 9
Cal handled 2/3rds of the transactions than Anthony handled
Cal = 2/3 × 99
Jade handled 16 more transactions than Cal.
Jade = 66 + 16
Jade handled = 82 transactions.
12. If a man buys 20 lollipops for $90 and sold them for $2 dollars determine his loss.
Cost of 20 lollipops = $90
Sold each lollipop for $2
So he sold 20 lollipops for $(20 × 2) = $40
Loss = $(90 – 40) = $50
Therefore, loss = $ 50.
13 . If C is a whole number, C+1 is a whole number after that. If A is a whole number, what is a whole number before that?
We know that the number ‘0’ together with the natural numbers gives us the numbers 0, 1, 2, 3, 4, 5, …………… which are called whole numbers.
If A is a whole number and it is greater than 0 then the whole number before that is A – 1, which will always be a whole number.
Again, when A is a whole number and it is equal to 0 then the whole number before that is A – 1 which means 0 – 1 = -1, which is not a whole number.
Therefore, if A is a whole number then the number before that will not always be a whole number.
14. Solve and leave answer in fraction
15. Divide the cancelling out all common factors
16. The annual cost of owning and operating a car, C dollars, is a linear function of the distance, d kilometers, it is driven.
c = md + b
The cost is $4600 for 10 000 km and $9100 for 25 000 km.
(a) Determine the values of m and b.
(b) Write c as a function of d.
c = md + b
The cost is $ 4600 for 10 000 km
4600 = m (10 000) + b
10 000 m + b = 4600
b = -10 000 m + 4600 ------- (i)
The cost is $ 9100 for 25 000 km
9100 = m (25 000) + b
9100 = 25 000 m + b
25 000 m + b = 9100
b = -25 000 m + 9100 --------- (ii)
From equation (i) and (ii) we get;
-10 000 m + 4600 = -25 000 m + 9100
-10 000 m + 25 000 m = 9100 – 4600
15 000 m = 4500
m = 4500/15 000
m = 3/10
m = 0.3
Now, put the value of m = 0.3 in equation (i) we get;
b = -10 000 (0.3) + 4600
b = -3000 + 4600
b = 1600
Answer: m = 0.3 and b = 1600
(b) c = md + b
m = 0.3
b = 1600
c = 0.3d + 1600
Answer: c = 0.3d + 1600
17. Solve using synthetic division or long division(x2 + 13x + 40) ÷ (x + 8)
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