Daily Practice · Higher Plus
October 2012 - Higher Plus 5-a-day
Every Higher Plus sheet published in October 2012, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' October 2012 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in October 2012
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st October 2012A block has mass 690 g (to the nearest 10 g) and volume 24 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 2nd October 2012Work out the nth term of the quadratic sequence 1, 8, 19, 34, ...
- 3rd October 2012y is directly proportional to sqrt(x). When x = 36, y = 12. Work out y when x = 49.
- 4th October 2012The point (20, 21) lies on the circle x^2 + y^2 = 841. Work out the gradient of the tangent to the circle at that point.
- 5th October 2012A bag holds 11 counters, r of them red. Two are taken without replacement and P(both red) = 3/55. Work out r.
- 6th October 2012On a histogram, a 5-wide bar and a 20-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 7th October 2012x = 137 and y = 64, each correct to the nearest whole number. Work out the upper bound of x - y.
- 8th October 2012The point (4, 2) lies on y = f(x). Write down its image on y = f(-x).
- 9th October 2012A train slows steadily from 30 m/s to rest in 4 seconds. Work out its deceleration.
- 10th October 2012In 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.
- 11th October 2012The probability of winning a game is 3/4. A player expects 18 wins. How many games did they play?
- 12th October 2012A histogram has two bars: one 10 units wide with frequency density 0.4, one 10 units wide with density 3.5. How many values in total?
- 13th October 2012A car covers 740 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.
- 14th October 2012Prove that the sum of 3 consecutive integers is always a multiple of 3. State the simplified sum you would use.
- 15th October 2012y is inversely proportional to x^2. When x = 3, y = 25. Work out y when x = 5.
- 16th October 2012In a vector proof you find that vector PQ = 3a + 3b and vector RS = 15a + 15b. What does this show about PQ and RS?
- 17th October 2012A bag holds 8 red and n blue counters. The probability of taking a red is 4/7. Work out n.
- 18th October 2012On a histogram, a 10-wide bar and a 20-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 19th October 2012Rationalise the denominator of 8/sqrt(2), giving your answer in its simplest form.
- 20th October 2012f(x) = 4x - 9 and g(x) = 4x - 5. Work out fg(0).
- 21st October 2012y is directly proportional to x^3. When x = 2, y = 32. Work out y when x = 5.
- 22nd October 2012A cuboid measures 4 cm by 7 cm by 5 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 23rd October 2012A bag holds 4 red and 4 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 24th October 2012A histogram has two bars: one 20 units wide with frequency density 0.4, one 5 units wide with density 0.6. How many values in total?
- 25th October 2012Simplify sqrt(12) + sqrt(3), giving your answer in the form a sqrt(b).
- 26th October 2012The curve y = sin x° is drawn for 0 <= x <= 360. Write down the value of y when x = 360.
- 27th October 2012y is directly proportional to sqrt(x). When x = 49, y = 63. Work out y when x = 81.
- 28th October 2012A cuboid measures 7 cm by 10 cm by 10 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 29th October 2012A bag holds 6 red, 5 blue and 4 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 30th October 2012On a histogram, a 4-wide bar and a 16-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 31st October 2012A rectangle is 20 cm by 28 cm, each correct to the nearest cm. Work out the upper bound of its area.