Daily Practice · Higher Plus
July 2005 - Higher Plus 5-a-day
Every Higher Plus sheet published in July 2005, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' July 2005 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in July 2005
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st July 2005A cuboid measures 13 cm by 9 cm by 15 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 2nd July 2005A bag holds 3 red and 6 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 3rd July 2005On a histogram, a 5-wide bar and a 20-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 4th July 2005A block has mass 280 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.
- 5th July 2005The point (3, 1) lies on y = f(x). Write down its image on y = f(-x).
- 6th July 2005y is directly proportional to x^3. When x = 2, y = 16. Work out y when x = 4.
- 7th July 2005A cuboid measures 11 cm by 9 cm by 10 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 8th July 2005A bag holds 6 red, 5 blue and 3 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 9th July 2005A histogram has two bars: one 5 units wide with frequency density 1.2, one 20 units wide with density 0.8. How many values in total?
- 10th July 2005x = 40 and y = 12, each correct to the nearest whole number. Work out the upper bound of x - y.
- 11th July 2005Prove that the sum of 5 consecutive integers is always a multiple of 5. State the simplified sum you would use.
- 12th July 2005y is directly proportional to sqrt(x). When x = 25, y = 20. Work out y when x = 81.
- 13th July 2005The 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.
- 14th July 2005A bag holds 11 counters, r of them red. Two are taken without replacement and P(both red) = 28/55. Work out r.
- 15th July 2005On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 16th July 2005A car covers 480 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.
- 17th July 2005f(x) = 4x + 3 and g(x) = 6x - 7. Work out fg(3).
- 18th July 2005A train slows steadily from 31 m/s to rest in 10 seconds. Work out its deceleration.
- 19th July 2005In 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.
- 20th July 2005The probability of winning a game is 3/8. A player expects 42 wins. How many games did they play?
- 21st July 2005A histogram has two bars: one 5 units wide with frequency density 2.5, one 5 units wide with density 1.4. How many values in total?
- 22nd July 2005Rationalise the denominator of 88/sqrt(11), giving your answer in its simplest form.
- 23rd July 2005The curve y = sin x° is drawn for 0 <= x <= 360. Write down the value of y when x = 0.
- 24th July 2005y is inversely proportional to x^2. When x = 5, y = 18. Work out y when x = 3.
- 25th July 2005In a vector proof you find that vector PQ = 5a + 4b and vector RS = 20a + 16b. What does this show about PQ and RS?
- 26th July 2005A bag holds 6 red and n blue counters. The probability of taking a red is 6/13. Work out n.
- 27th July 2005On a histogram, a 10-wide bar and a 20-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 28th July 2005Simplify sqrt(27) + sqrt(3), giving your answer in the form a sqrt(b).
- 29th July 2005A quadratic sequence starts 6, 9, 14, 21. Work out the second difference, and the coefficient of n^2.
- 30th July 2005y is directly proportional to x^3. When x = 2, y = 48. Work out y when x = 5.
- 31st July 2005A cuboid measures 12 cm by 5 cm by 11 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.