Download Module 5 Higher Year 11 Spring 496.50KB 2017

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Module 5 Higher Homework
Module 5 Homework 3: Non-Calculator
16
23
is greater than
24
36
b) Copy and complete the following;
2
i) =
(1)
3
36
9
108
ii) =
(1)
4
c) Factorise; 28x + 52 (1)
1) a) Show that
(2)
2) Look at the following diagram;
100
a) Write down the size of angle x and explain
how you worked it out
(2)
b) Calculate the size of angle y (2)
o
xo
yo
30o
3)
-3
-2
-1
0
1
2
3
4
a) Write down the integers that satisfy this
inequality (2)
b) Solve the inequality; 3x – 1 < 7 – x (2)
c) Write a non-integer value which satisfies
both the inequality diagram and part b) (1)
4) Look at the following solid;
a) Draw the plan view (1)
b) Draw the side elevation (1)
c) Write down the name of the 2D shape
That can be seen from the front view (1)
d) Work out the area of the base (2)
front
10cm
20cm
5) Peter has x money in his bank account. His brother, Sam has four times as much
money as Peter in his bank account.
a) Write an expression in terms of x for the amount of money Sam has (1)
b) The difference between the money Peter has and the money Sam has is equal to £60.
Use this information to write an equation in terms of x. (2)
c) Solve this equation to work out how much money Peter has in his bank account (2)
6 a) Multiply out -3(3x + 2) (1)
b) Work out the value of -3(3x + 2) + xy when x = 2 and y = 15
7 a) Factorise; x2 + 3x + 2
(2)
b) Hence solve x2 + 3x + 2 = 0
(2)
(3)
6m
4m
8) Work out the area of the triangle shown; (2)
10m
2
Module 5 Higher Homework
9 a) Work out 63 (2)
b) Work out the value of 65 ÷ 63 (2)
c) Multiply out a(a + b) (1)
d) Multiply out and simplify; 2(a – 1) + 3a – 1
(2)
10) A formula is given as
p = 2q + 1
3
a) Find the value of p when q = 4 (1)
b) Rearrange the formula to make q the subject (3)
11) A formula is given as t = s2
a) Rearrange the formula to make s the subject (1)
b) Estimate the value of s when t = 70 (3)
12 a) Draw the graph of y = x + 2 for values of x between -3 and 3. (2)
b) Draw the graph of y = x2 on the same set of axes as a) (2)
c) Hence, or otherwise, find the solutions to the equation; x2 = x + 2 (2)
13) Solve; 2(x – 1) = 3
(2)
14) This is the net of a cuboid where each square is 1cm2
a) Work out the total
surface area of the net (2)
b) Work out the volume of
the cuboid formed by
folding the net (3)
15) Here is part of a number grid;
1
9
17
25
33
2
10
18
26
34
3
11
19
27
35
4
12
20
28
36
5
13
21
29
37
6
14
22
30
38
7
15
23
31
39
8
16
24
32
40
The shaded shape is called T11
because it has the number 11 at
the top. The sum of the numbers
in T11 is called Sum(T11).
a) Work out Sum(T11) (1)
b) Work out Sum(T22) (1)
c) Copy and complete the empty shaded boxes for Tn.
(2)
d) Write down an expression for Sum(Tn) (2)
e) Show that Sum(Tn ) – 1 will always be a multiple of 5. (2)
n
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Module 5 Higher Homework
Module 5 Homework 4: Calculator
1 a) Calculate the area of the following composite shape;
(3)
b) Calculate the perimeter (2)
4.7 cm
5.3 cm
2.5 cm
7.2 cm
2) Solve each of these equations;
a) 4x – 1 = 2 – 2x (3)
b) 4a + 2 = 5
(3)
6
3)
y
4
3
Copy the set of axes and shape A
A
2
1
-5
-4 -3 -2
-1 0
-1
1 2
3
4
5 x
a) Reflect shape A in the x axis (2)
b) Translate shape A four units to the left
and five units down. (1)
c) Rotate shape A 90o anti-clockwise about
the origin. (2)
-2
-3
-4
4 a) Draw the graph of y = ½x for values of x from -2 to 4 (2)
b) Hence shade the region on your graph expressed by the inequality y ≤ ½x (2)
c) Write down the integer values which satisfy the inequality -2 ≤ x < 4 (2)
xo
5) This is an irregular pentagon. Calculate the
size of angle of x (4)
6) Simplify;
a) 3x2y + 2x2y
b) 2xy3 × 3x3y2
c) (3x)3 (2)
65
85o
o
110o
(1)
(2)
A
7) The diagram shows rectangle ABCD.
Side AB is decreased by 5%
Side BD is increased by 5%
Calculate the area of the new rectangle. (3) C
8 a) Factorise 3x2 + 7x + 2 (2)
b) Hence simplify; 3x2 + 7x + 2
(x + 2)
135o
(2)
20cm
B
10cm
D
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Module 5 Higher Homework
9) The area of a circle is п × r2, where п is approximately 3.14 and r is the radius
The circumference of a circle is п × D, where D is the diameter
a) Calculate the area of a circle with radius 20 cm (use 3.14 as the value of п) (2)
b) Calculate the circumference of the same circle (2)
c) Given that C = п D, rearrange the formula to make D the subject (1)
d) Calculate the diameter of a circle with a circumference of 12.5cm (1)
10) Calculate the size of angles, m, n, and p
(3)
Not to scale
20o
p
20o
20o
m
n
11) A formula is given as; p = ½q – 2
a) Calculate p when q = 6 (1)
b) Rearrange the formula to make q the subject (2)
c) Calculate q when p = 2⅓ (1)
12) The population density of town A is given as 4500 people per square kilometre.
a) Calculate the population of town A if the total area is 122.5 km2 (2)
b) Calculate the number of people who live in every 100m2?
(2)
c) The population of town B is 39,000 people. The town has an area of 8.5 km2.
i) Write the area of town B as a percentage of the area of town A (2)
ii) Show which town has the greater population density. (2)
13)
a) Draw an enlargement of shape A using scale
factor 2 (2)
b) Copy the diagram and rotate shape A 90o
clockwise using the centre of rotation shown.
(2)
A
14) A rocket is travelling at an average speed of 200 metres per second
a) Calculate the speed of the rocket in kilometres per hour (3)
b) Use the conversion 5 miles = 8 km to write your answer in miles per hour (2)
c) How long to the nearest minute would it take the rocket to travel a distance of 250
km? (2)
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Module 5 Higher Homework
Module 5 Homework 5: Non-Calculator
1)
4.5cm
2)
4cm
a) Work out the area of the parallelogram (2)
b) Work out the perimeter of the parallelogram (2)
6 cm
6 cm
The diagram shows a regular dodecagon.
a) Write down the length of one side
(1)
b) Work out the area of the dodecagon given the dimensions
shown (3)
3) Here is a sequence;
14 11 8 5
a) Write down the next two terms in the sequence (2)
b) Write down the term-to-term rule
(1)
th
c) Write down an expression for the n term in the sequence (2)
d) The nth term in a sequence is given as n2 + 1. Write down the first 3 terms in the
sequence
(2)
4 a) Simplify; 7g + g – 2 + 3 – 4f – 10 + f
(3)
b) Given that a = 2, b = ¼ and c = 3 work out the value of; ac + 8b
c) Solve 4x + 5 = 6x + 4
(3)
d) Solve 0.3r = 3 (2)
(3)
5) A house costs £210 000 at the start of 2005. By the end of each year the cost has
increased by 10%. Work out the cost of the house at the end of 2007.
(3)
x
 6 (1)
6 a) Solve
3
b) Solve 2(x + 1) = 10 (2)
7)
Line ABC is a tangent to the circle with centre O.
a) Calculate the size of angle DEB and state which
circle theorem allows you to work it out (2)
b) Calculate angle ODE (2)
c) Calculate angle DBE (2)
d) Calculate angle DOB (2)
8) Shaded and unshaded triangles are used to
make a sequence of patterns;
Pattern 1
Pattern 2
a) How many black triangles
will be in pattern 4? (1)
b) How many triangles will there
be in total in pattern 6? (2)
Pattern 3 c) There will be n(n  1) white triangles
2
in pattern n. Write down an
expression for the number of white
triangles in pattern (n + 1) (2)
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Module 5 Higher Homework
9 a) Solve
6x – 2 = 2x – 5
(3)
b) Expand and simplify 3(2a – b) – 2(a – 2b)
c) Factorise fully; 24ab + 16b (2)
(3)
10 a) Simplify (57 × 54) ÷ 53 (2)
2 y 3  12 z 2
b) Simplify fully
(3)
6y2z
11) Given the points A(0, 5) B(3, 11) work out each of the following;
a) length AB (3)
b) the gradient of AB
(2)
c) the equation of the line AB
(1)
12)
10cm
(2x + 1)cm
x cm
a) Write an expression for the volume
of the cuboid
(3)
b) Find the value of x given that the
volume is 60cm3 (3)
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Module 5 Higher Homework
Module 5 Homework 6: Calculator
1) The wheel of a car has a radius of 20 cm.
a) Work out the circumference of the wheel (2)
b) Work out how many revolutions of the wheel there would be if the car travels 10
metres (3)
2 a) Draw the graph of y = x2 + x – 1 for values of x from -2 to 2.
b) Hence solve the equation x2 + x – 1 = 1
(1)
(4)
3) Two of the interior angles of a pentagon are x and 2x. The sum of the remaining 3
angles is 7x. Calculate the value of x.
(3)
4) Square Rectangle Rhombus Parallelogram Kite Trapezium
a) Name two quadrilaterals with four sides of equal lengths and where the diagonals
are perpendicular bisectors of each other.
(2)
b) Name a quadrilateral with just one pair of parallel sides (1)
c) Describe the properties of a parallelogram
(2)
d) Name the three quadrilaterals which have a rotational symmetry of order 2. (2)
5 a) Expand 3(y + 2)
(1)
b) Expand and simplify; x(x + 2) – 2(x2 – 2)
6)
8m
(3)
A rope is tied to the top of a pole. It is attached to the
ground 10 metres away from the foot of the pole.
Calculate the length of the rope.
(3)
10m
7)
1 2 3 4
6 7 8 9
11 12 13 14
16 17 18 19
21 22 23 24
5
10
15
20
25
Here is part of a number grid. The shaded shape is called X1 because it has
the number 1 in the top left
a) Write the sum of the numbers in X1 (1)
b) Write the sum of the numbers in X12 (1)
c) Copy and complete the empty boxes for Xn (2)
n
d) Write down an expression for the sum of the values in Xn (2)
e) Show that the sum of the values in Xn will always be even
(2)
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Module 5 Higher Homework
8) COE
A
a) Copy the diagram and draw an enlargement of
triangle ABC, scale factor 2 using the centre of
enlargement as shown (2)
b) Copy the diagram again and translate triangle
ABC using the vector  5  (2)
C
B
  3
 
c) Reflect triangle ABC in the line y = 1 (2)
9 a) Draw the region defined by the inequality y ≤ 2x (3)
b) On the same diagram identify the region bounded by the inequalities; y ≤ 2x, y > 0
and x ≤ 4 (3)
c) Write down the integers which satisfy the inequality -10 < n < -2 (1)
10) Simplify;
3x 2 x x


2
3 4
20cm
(3)
11) The diameter of a cylinder is 20cm. The height of the
cylinder is 12 cm. 1 litre = 1000 cm3.
Work out the capacity of the cylinder in litres. (4)
12)
z
30
12 cm
a) Work out the size of angle c (2)
b) Work out the size of angle z (3)
o
13) Simplify fully
2 x 2  5x  2
4x 2 1
(3)
14) a, b, c, d and e represent lengths. Arrange the 8 expressions in the table under
the correct heading.
(4)
Length
Area
Volume
ab
2c
3c + 2d
cde
d–e
ab2
½bc
 d2
15) ABCDEF is a regular hexagon. Work out the value of x. (3)
F
A
B
x
C
E
D