Daily Practice · Higher Plus
July 2012 - Higher Plus 5-a-day
Every Higher Plus sheet published in July 2012, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' July 2012 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in July 2012
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st July 2012A bag holds 4 red, 6 blue and 6 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 2nd July 2012On 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?
- 3rd July 2012Expand and simplify (5 + sqrt(10))(5 - sqrt(10)).
- 4th July 2012Prove that the sum of 9 consecutive integers is always a multiple of 9. State the simplified sum you would use.
- 5th July 2012A train slows steadily from 17 m/s to rest in 5 seconds. Work out its deceleration.
- 6th July 2012The point (9, 40) lies on the circle x^2 + y^2 = 1681. Work out the gradient of the tangent to the circle at that point.
- 7th July 2012A bag holds 9 counters, r of them red. Two are taken without replacement and P(both red) = 1/36. Work out r.
- 8th July 2012A histogram has two bars: one 10 units wide with frequency density 2, one 10 units wide with density 3. How many values in total?
- 9th July 2012A block has mass 550 g (to the nearest 10 g) and volume 10 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 10th July 2012f(x) = 3x - 4 and g(x) = 6x + 7. Work out fg(0).
- 11th July 2012y is inversely proportional to x^2. When x = 2, y = 75. Work out y when x = 5.
- 12th July 2012In a circle theorem proof, a step uses the fact that the three angles of triangle OAB are being summed. State the reason being quoted.
- 13th July 2012The probability of winning a game is 4/5. A player expects 20 wins. How many games did they play?
- 14th July 2012On 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?
- 15th July 2012x = 128 and y = 22, each correct to the nearest whole number. Work out the upper bound of x - y.
- 16th July 2012The curve y = sin x° is drawn for 0 <= x <= 360. Write down the value of y when x = 360.
- 17th July 2012y is directly proportional to x^3. When x = 2, y = 32. Work out y when x = 3.
- 18th July 2012In a vector proof you find that vector PQ = 3a - 5b and vector RS = 12a - 20b. What does this show about PQ and RS?
- 19th July 2012A bag holds 5 red and n blue counters. The probability of taking a red is 1/2. Work out n.
- 20th July 2012A histogram has two bars: one 20 units wide with frequency density 1.2, one 10 units wide with density 0.6. How many values in total?
- 21st July 2012A car covers 890 m (to the nearest 10 m) in 9 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 22nd July 2012A quadratic sequence starts 12, 32, 62, 102. Work out the second difference, and the coefficient of n^2.
- 23rd July 2012y is directly proportional to sqrt(x). When x = 36, y = 18. Work out y when x = 16.
- 24th July 2012A cuboid measures 4 cm by 12 cm by 8 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 25th July 2012A 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?
- 26th July 2012On a histogram, a 10-wide bar and a 20-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 27th July 2012Rationalise the denominator of 9/sqrt(3), giving your answer in its simplest form.
- 28th July 2012Solve x^2 + 11x + 28 > 0.
- 29th July 2012A train slows steadily from 35 m/s to rest in 4 seconds. Work out its deceleration.
- 30th July 2012A cuboid measures 12 cm by 4 cm by 8 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 31st July 2012A bag holds 3 red, 3 blue and 6 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?