Daily Practice · Higher Plus
October 2006 - Higher Plus 5-a-day
Every Higher Plus sheet published in October 2006, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' October 2006 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in October 2006
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st October 2006A bag holds 6 red, 7 blue and 5 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 2nd October 2006On a histogram, a 5-wide bar and a 20-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 3rd October 2006Expand and simplify (4 + sqrt(5))(4 - sqrt(5)).
- 4th October 2006Simplify (x^2 - 5x - 14)/(x + 2).
- 5th October 2006y is directly proportional to x^3. When x = 4, y = 384. Work out y when x = 2.
- 6th October 2006The point (8, 15) lies on the circle x^2 + y^2 = 289. Work out the gradient of the tangent to the circle at that point.
- 7th October 2006A bag holds 8 counters, r of them red. Two are taken without replacement and P(both red) = 5/14. Work out r.
- 8th October 2006A histogram has two bars: one 10 units wide with frequency density 2.5, one 25 units wide with density 3. How many values in total?
- 9th October 2006A block has mass 770 g (to the nearest 10 g) and volume 7 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 10th October 2006In an algebraic proof, how would you write an even number in terms of an integer n?
- 11th October 2006y is directly proportional to sqrt(x). When x = 25, y = 10. Work out y when x = 4.
- 12th October 2006In a circle theorem proof, a step uses the fact that a tangent meets a radius at the point of contact. State the reason being quoted.
- 13th October 2006The probability of winning a game is 1/2. A player expects 10 wins. How many games did they play?
- 14th October 2006On a histogram, a 5-wide bar and a 10-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 15th October 2006x = 60 and y = 21, each correct to the nearest whole number. Work out the upper bound of x - y.
- 16th October 2006Make x the subject of 5x + 4 = y(x + 4).
- 17th October 2006A train slows steadily from 37 m/s to rest in 8 seconds. Work out its deceleration.
- 18th October 2006In a vector proof you find that vector PQ = a + b and vector RS = 2a + 2b. What does this show about PQ and RS?
- 19th October 2006A bag holds 3 red and n blue counters. The probability of taking a red is 1/2. Work out n.
- 20th October 2006A histogram has two bars: one 10 units wide with frequency density 2, one 5 units wide with density 0.8. How many values in total?
- 21st October 2006A car covers 120 m (to the nearest 10 m) in 7 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 22nd October 2006Write 7/(x + 4) + 4/(x - 2) as a single fraction.
- 23rd October 2006y is inversely proportional to x^2. When x = 3, y = 16. Work out y when x = 4.
- 24th October 2006A cuboid measures 7 cm by 11 cm by 3 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 25th October 2006A bag holds 5 red and 3 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 26th October 2006On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 27th October 2006Rationalise the denominator of 42/sqrt(6), giving your answer in its simplest form.
- 28th October 2006Solve 4x^2 - 13x - 12 = 0.
- 29th October 2006y is directly proportional to x^3. When x = 3, y = 54. Work out y when x = 5.
- 30th October 2006A cuboid measures 7 cm by 7 cm by 9 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 31st October 2006A bag holds 6 red, 7 blue and 3 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?