1. Yr 12 C1 Quiz A
Green Question = 3 points
Red Question = 1 point

3. 1.
Red Question
Green Question

4. 2.
Red Question
Green Question
Which are correct ?
Simplify

5. 3.
There are two Barbers in Riddletown. One is sloppy and expensive, the other is neat and charges a fair price.
David goes to a Barber every week. He always uses the sloppy expensive Barber. Why?
What travels around the world but stays in the corner?

6. 4.
Calculate
Simplify

7. 5.
Differentiate with respect to x
Differentiate with respect to x

8. 1
𝟕 𝟓 2
True
𝒂 𝒃 = 𝒂𝒃
𝒂 𝒃 = 𝒂 𝒃 3
a stamp 4 𝟏𝟔 5
𝟏 𝟐 𝒙 −𝟏/𝟐 −𝟏𝟖 𝒙 −𝟒 1
𝟕+𝟑 𝟓 2
𝟕 𝟒 3
David is the other Barber 4
𝟓 𝒙 −𝟒/𝟑 5
𝟏−𝟏𝟔 𝒙 −𝟐

10. 4𝑥−3>7−𝑥 4𝑥−3>7−𝑥 2𝑥 2 −5𝑥−12<0 6.
Find the set of values for which
BOTH
4𝑥−3>7−𝑥
4𝑥−3>7−𝑥
AND
2𝑥 2 −5𝑥−12<0
Hints:
Draw a graph
Use a number line

11. 7.
Write in completed square, then sketch showing the minimum point:
Sketch showing the intersections on the axes:
𝑦=6 𝑥 2 −𝑥−12
𝑦=− 𝑥 2 −4𝑥+1
Type equation here.

12. What has a face and two hands but no arms or legs?8.
Jenny puts down her iron and gets £100. Shelly parks her car at Liverpool Street Station and immediately goes Bankrupt. What is going on?
What has a face and two hands but no arms or legs?

13. 9. Show that the point P (-3, 11) lies on L
Show that the point
P (-3, 11) lies on L
Find an equation of the line perpendicular to L which passes through point P
Write your answer in the form y=𝑚𝑥+𝑐

14. 10. Point Q on curve C has x-coordinate equal to 2
Point Q on curve C has x-coordinate equal to 2
Find the gradient of the tangent to C at point Q
Find the equation of the normal to C at point Q
Write your answer in the form 𝑎𝑥+𝑏𝑦=𝑐

15. 6
𝒙>𝟐 7
Points − 𝟒 𝟑 , 𝟎 and 𝟑 𝟐 , 𝟎 8
a clock 9
𝟓−𝟐 −𝟑 =𝟓+𝟔=𝟏𝟏 10 −𝟐 6
𝟐<𝒙<𝟒 7
Max Point −𝟐, 𝟓 8
they are playing monopoly 9
𝒚= 𝟏 𝟐 𝒙+ 𝟐𝟓 𝟐 10
𝒙−𝟐𝒚=𝟖

17. log (2−3𝑥) −2 log 𝑥 =2 3 log 4𝑥 −2 log 𝑥 11. Solve
Find both values of x
3 log 4𝑥 −2 log 𝑥
Simplify

18. 12.
𝑝= 𝑙𝑜𝑔 2 𝑥 and 𝑞= 𝑙𝑜𝑔 2 𝑦
Write the following as an expression in 𝑝 and 𝑞
(with no logarithms)
𝑙𝑜𝑔 2 𝑥 𝑦 3 + 𝑙𝑜𝑔 2 16
Write the following as a single expression in 𝑝 and 𝑞
𝑙𝑜𝑔 2 𝑥 2 − 𝑙𝑜𝑔 2 𝑦

19. What word begins and ends with an e but contains only one letter?
13.
A frog has fallen into a pit. Each day the frog climbs 3 m
And then falls back 2m at night.
How many days does it take the frog to escape the pit?
What word begins and ends with an e
but contains only one letter?

20. 14.
Sketch the graph of y = -f(x)
Sketch the graph of y = f(x+4)

21. 𝑥 2 + 𝑦 2 =10 𝑦=𝑥−4 𝑦= 𝑥 2 +6𝑥+2 𝑦=𝑥−2 15. Find where the curve
Solve the simultaneous equations
Find where the curve
𝑥 2 + 𝑦 2 =10
𝑦=𝑥−4
Meets the line
𝑦= 𝑥 2 +6𝑥+2
𝑦=𝑥−2

22. 1
𝒍𝒐𝒈 𝟔𝟒𝒙 2
𝟐𝒑 𝒒 3
An Envelope 4
Points 𝟎, −𝟑 and 𝟐, 𝟎 5
−𝟐, −𝟔 and −𝟑, −𝟕 1
𝒙= 𝟏 𝟐 , 𝒙=−𝟐 2
𝒑−𝟑𝒒+𝟒 3
28 days to escape 4
Points −𝟒, 𝟑 and −𝟐, 𝟎 5
−𝟏, −𝟑 and 𝟑, 𝟏

24. 16.
Find
Find
𝟎 𝟏 𝟑 𝒙 𝟐 − 𝒙 𝟑 𝒙 𝒅𝒙
𝟑 𝒙 𝟐 −𝟕 𝒅𝒙

25. 17. Form an equation in p Find the two possible values of p
Form an equation in p Find the two possible values of p
State the discriminant and its value for equal roots

26. 18. Which number should go in the empty triangle?
It occurs once in every minute
Twice in every moment
And yet never in one hundred thousand years

27. 19. Find 𝑓(𝑥) Find an equation for the tangent to C at point P,
Find 𝑓(𝑥)
Find an equation for the tangent to C at point P,
Write your answer in the form 𝑎𝑥+𝑏𝑦=𝑐

28. Find the gradient of the curve when 𝑥=−1
20.
Find the gradient of the curve when 𝑥=−1
Find the two stationary points and determine which one is a local maximum

29. 1
𝟑𝟐 𝟑𝟓 2
𝒃 𝟐 −𝟒𝒂𝒄=𝟎 3
The letter M 4
f(x) = 𝒙 𝟐 −𝟔𝒙+ 𝟖 𝒙 +𝟏 5
𝒅𝒚 𝒅𝒙 =𝟑 𝒙 𝟐 −𝟓𝒙−𝟐
gradient is 6 1
𝒙 𝟑 −𝟕𝒙+𝑪 2
𝟒 𝒑 𝟐 −𝟏𝟐𝒑−𝟏𝟔=𝟎
𝒑=𝟒 𝒐𝒓 𝒑=−𝟏 3
5 (add the two bottom numbers, divide by the top) 4
𝟒𝒙−𝒚=𝟔 5
𝟐, −𝟓 minimum
− 𝟏 𝟑 , 𝟒 𝟑 maximum

31. Point A is where the lines
𝑦=3𝑥−9 and 𝑥+2𝑦+4=0 intersect
Point B is where the lines
𝑦=1− 𝑥 2 and 2𝑦+3𝑥=12 intersect
Find distance AB and give your answer as a simplified surd

32. 𝐴 𝑖𝑠 5, − 𝐵 𝑖𝑠 2, −3
Distance AB is − = = =