Daily Practice · Higher Plus
April 2009 - Higher Plus 5-a-day
Every Higher Plus sheet published in April 2009, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' April 2009 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in April 2009
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st April 2009On a histogram, a 4-wide bar and a 16-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 2nd April 2009Simplify sqrt(45) + sqrt(180), giving your answer in the form a sqrt(b).
- 3rd April 2009Work out the coordinates of the turning point of y = x^2 + 6x - 15.
- 4th April 2009y is directly proportional to x^3. When x = 2, y = 16. Work out y when x = 4.
- 5th April 2009In a vector proof you find that vector PQ = 3a + 2b and vector RS = 12a + 8b. What does this show about PQ and RS?
- 6th April 2009A bag holds 7 red and n blue counters. The probability of taking a red is 7/12. Work out n.
- 7th April 2009A histogram has two bars: one 10 units wide with frequency density 2, one 20 units wide with density 0.8. How many values in total?
- 8th April 2009A rectangle is 21 cm by 5 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 9th April 2009Simplify (x^2 - 4x - 12)/(x + 2).
- 10th April 2009y is directly proportional to sqrt(x). When x = 36, y = 12. Work out y when x = 49.
- 11th April 2009A cuboid measures 5 cm by 11 cm by 10 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 12th April 2009A bag holds 5 red and 4 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 13th April 2009On a histogram, a 5-wide bar and a 10-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 14th April 2009Expand and simplify (8 + sqrt(6))(8 - sqrt(6)).
- 15th April 2009In an algebraic proof, how would you write three consecutive integers in terms of an integer n?
- 16th April 2009A train slows steadily from 32 m/s to rest in 4 seconds. Work out its deceleration.
- 17th April 2009A cuboid measures 9 cm by 11 cm by 6 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 18th April 2009A bag holds 3 red, 6 blue and 5 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 19th April 2009A histogram has two bars: one 10 units wide with frequency density 1.5, one 5 units wide with density 3.5. How many values in total?
- 20th April 2009A block has mass 850 g (to the nearest 10 g) and volume 23 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 21st April 2009Make x the subject of 6x + 4 = y(x + 4).
- 22nd April 2009y is inversely proportional to x^2. When x = 4, y = 9. Work out y when x = 3.
- 23rd April 2009The point (6, 8) lies on the circle x^2 + y^2 = 100. Work out the gradient of the tangent to the circle at that point.
- 24th April 2009A bag holds 6 counters, r of them red. Two are taken without replacement and P(both red) = 2/5. Work out r.
- 25th April 2009On a histogram, a 5-wide bar and a 10-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 26th April 2009x = 106 and y = 13, each correct to the nearest whole number. Work out the upper bound of x - y.
- 27th April 2009Write 4/(x + 2) + 2/(x + 5) as a single fraction.
- 28th April 2009y is directly proportional to x^3. When x = 2, y = 16. Work out y when x = 5.
- 29th April 2009In a circle theorem proof, a step uses the fact that a radius is drawn to the midpoint of a chord. State the reason being quoted.
- 30th April 2009The probability of winning a game is 1/8. A player expects 15 wins. How many games did they play?