Daily Practice · Higher Plus
July 2006 - Higher Plus 5-a-day
Every Higher Plus sheet published in July 2006, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' July 2006 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in July 2006
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st July 2006y is directly proportional to x^3. When x = 2, y = 16. Work out y when x = 3.
- 2nd July 2006A cuboid measures 13 cm by 13 cm by 4 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 3rd July 2006A bag holds 3 red, 3 blue and 5 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 4th July 2006A histogram has two bars: one 5 units wide with frequency density 0.4, one 5 units wide with density 1.4. How many values in total?
- 5th July 2006A rectangle is 14 cm by 24 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 6th July 2006Make x the subject of 7x + 7 = y(x + 7).
- 7th July 2006y is directly proportional to sqrt(x). When x = 49, y = 63. Work out y when x = 4.
- 8th July 2006The point (5, 12) lies on the circle x^2 + y^2 = 169. Work out the gradient of the tangent to the circle at that point.
- 9th July 2006A bag holds 10 counters, r of them red. Two are taken without replacement and P(both red) = 2/9. Work out r.
- 10th July 2006On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 11th July 2006Expand and simplify (8 + sqrt(7))(8 - sqrt(7)).
- 12th July 2006Write 6/(x - 1) + 4/(x) as a single fraction.
- 13th July 2006A train slows steadily from 14 m/s to rest in 4 seconds. Work out its deceleration.
- 14th July 2006In a circle theorem proof, a step uses the fact that two tangents are drawn to a circle from the same external point. State the reason being quoted.
- 15th July 2006The probability of winning a game is 5/8. A player expects 55 wins. How many games did they play?
- 16th July 2006A histogram has two bars: one 5 units wide with frequency density 2, one 10 units wide with density 1.4. How many values in total?
- 17th July 2006A block has mass 600 g (to the nearest 10 g) and volume 19 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 18th July 2006Solve 9x^2 - 6x + 1 = 0.
- 19th July 2006y is inversely proportional to x^2. When x = 3, y = 50. Work out y when x = 5.
- 20th July 2006In a vector proof you find that vector PQ = 3a - 4b and vector RS = 6a - 8b. What does this show about PQ and RS?
- 21st July 2006A bag holds 5 red and n blue counters. The probability of taking a red is 5/7. Work out n.
- 22nd July 2006On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 23rd July 2006x = 198 and y = 183, each correct to the nearest whole number. Work out the upper bound of x - y.
- 24th July 2006f(x) = 3x + 9. Work out the inverse function f^-1(x).
- 25th July 2006y is directly proportional to x^3. When x = 2, y = 32. Work out y when x = 3.
- 26th July 2006A cuboid measures 7 cm by 12 cm by 12 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 27th July 2006A bag holds 4 red and 6 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 28th July 2006A histogram has two bars: one 20 units wide with frequency density 1.2, one 10 units wide with density 3.5. How many values in total?
- 29th July 2006A car covers 690 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.
- 30th July 2006Solve x^2 + y^2 = 169 and y = x - 7 simultaneously.
- 31st July 2006y is directly proportional to sqrt(x). When x = 25, y = 20. Work out y when x = 64.