Daily Practice · Higher Plus
October 2010 - Higher Plus 5-a-day
Every Higher Plus sheet published in October 2010, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' October 2010 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in October 2010
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st October 2010f(x) = 4x + 4. Work out the inverse function f^-1(x).
- 2nd October 2010y is inversely proportional to x^2. When x = 5, y = 32. Work out y when x = 4.
- 3rd October 2010A cuboid measures 5 cm by 3 cm by 5 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 4th October 2010A 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?
- 5th October 2010On a histogram, a 5-wide bar and a 10-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 6th October 2010A rectangle is 26 cm by 5 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 7th October 2010Solve x^2 + y^2 = 841 and y = x + 1 simultaneously.
- 8th October 2010y is directly proportional to x^3. When x = 3, y = 81. Work out y when x = 5.
- 9th October 2010A cuboid measures 10 cm by 8 cm by 4 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 10th October 2010A bag holds 5 red, 4 blue and 3 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 11th October 2010A histogram has two bars: one 20 units wide with frequency density 1.2, one 5 units wide with density 0.6. How many values in total?
- 12th October 2010Expand and simplify (9 + sqrt(10))(9 - sqrt(10)).
- 13th October 2010Use the iteration x(n+1) = cube root of (5x(n) + 1) with x(0) = 5. Work out x(1) to 3 decimal places.
- 14th October 2010y is directly proportional to sqrt(x). When x = 9, y = 6. Work out y when x = 4.
- 15th October 2010The point (3, 4) lies on the circle x^2 + y^2 = 25. Work out the gradient of the tangent to the circle at that point.
- 16th October 2010A bag holds 5 counters, r of them red. Two are taken without replacement and P(both red) = 3/10. Work out r.
- 17th October 2010On 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?
- 18th October 2010A block has mass 350 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.
- 19th October 2010Work out the nth term of the quadratic sequence 11, 22, 41, 68, ...
- 20th October 2010A train slows steadily from 39 m/s to rest in 10 seconds. Work out its deceleration.
- 21st October 2010In a circle theorem proof, a step uses the fact that a triangle is drawn from the ends of a diameter to a point on the circle. State the reason being quoted.
- 22nd October 2010The probability of winning a game is 7/8. A player expects 21 wins. How many games did they play?
- 23rd October 2010A histogram has two bars: one 5 units wide with frequency density 1.2, one 20 units wide with density 3.5. How many values in total?
- 24th October 2010x = 44 and y = 5, each correct to the nearest whole number. Work out the upper bound of x - y.
- 25th October 2010The point (2, -4) lies on y = f(x). Write down its image on y = f(x - 5).
- 26th October 2010y is inversely proportional to x^2. When x = 5, y = 64. Work out y when x = 4.
- 27th October 2010In a vector proof you find that vector PQ = 6a + 3b and vector RS = 24a + 12b. What does this show about PQ and RS?
- 28th October 2010A bag holds 7 red and n blue counters. The probability of taking a red is 1/2. Work out n.
- 29th October 2010On a histogram, a 10-wide bar and a 30-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 30th October 2010A car covers 350 m (to the nearest 10 m) in 4 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 31st October 2010Prove that the sum of 5 consecutive integers is always a multiple of 5. State the simplified sum you would use.