Daily Practice · Higher Plus
June 2007 - Higher Plus 5-a-day
Every Higher Plus sheet published in June 2007, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' June 2007 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in June 2007
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st June 2007Solve x^2 + y^2 = 25 and y = x + 1 simultaneously.
- 2nd June 2007y is directly proportional to x^3. When x = 3, y = 54. Work out y when x = 2.
- 3rd June 2007The 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.
- 4th June 2007A bag holds 5 counters, r of them red. Two are taken without replacement and P(both red) = 1/10. Work out r.
- 5th June 2007A histogram has two bars: one 10 units wide with frequency density 1.2, one 20 units wide with density 0.8. How many values in total?
- 6th June 2007A rectangle is 28 cm by 4 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 7th June 2007Use the iteration x(n+1) = cube root of (12x(n) + 3) with x(0) = 2. Work out x(1) to 3 decimal places.
- 8th June 2007y is directly proportional to sqrt(x). When x = 4, y = 18. Work out y when x = 25.
- 9th June 2007In a circle theorem proof, a step uses the fact that the three angles of triangle OAB are being summed. State the reason being quoted.
- 10th June 2007The probability of winning a game is 2/5. A player expects 16 wins. How many games did they play?
- 11th June 2007On a histogram, a 4-wide bar and a 12-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 12th June 2007Expand and simplify (8 + sqrt(7))(8 - sqrt(7)).
- 13th June 2007Work out the nth term of the quadratic sequence 3, 14, 31, 54, ...
- 14th June 2007A train slows steadily from 26 m/s to rest in 10 seconds. Work out its deceleration.
- 15th June 2007In a vector proof you find that vector PQ = 5a + 5b and vector RS = 15a + 15b. What does this show about PQ and RS?
- 16th June 2007A bag holds 5 red and n blue counters. The probability of taking a red is 5/13. Work out n.
- 17th June 2007A histogram has two bars: one 20 units wide with frequency density 1.2, one 5 units wide with density 3.5. How many values in total?
- 18th June 2007A block has mass 820 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.
- 19th June 2007The point (4, -2) lies on y = f(x). Write down its image on y = -f(x).
- 20th June 2007y is inversely proportional to x^2. When x = 4, y = 9. Work out y when x = 3.
- 21st June 2007A cuboid measures 14 cm by 5 cm by 12 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 22nd June 2007A 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?
- 23rd June 2007On a histogram, a 5-wide bar and a 10-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 24th June 2007x = 126 and y = 112, each correct to the nearest whole number. Work out the upper bound of x - y.
- 25th June 2007Prove that the sum of 3 consecutive integers is always a multiple of 3. State the simplified sum you would use.
- 26th June 2007y is directly proportional to x^3. When x = 3, y = 81. Work out y when x = 5.
- 27th June 2007A cuboid measures 11 cm by 9 cm by 12 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 28th June 2007A bag holds 7 red, 4 blue and 6 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 29th June 2007A histogram has two bars: one 5 units wide with frequency density 1.5, one 5 units wide with density 3. How many values in total?
- 30th June 2007A car covers 250 m (to the nearest 10 m) in 3 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.