Daily Practice · Higher Plus
September 2006 - Higher Plus 5-a-day
Every Higher Plus sheet published in September 2006, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' September 2006 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in September 2006
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st September 2006A bag holds 5 red, 5 blue and 3 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 2nd September 2006A histogram has two bars: one 5 units wide with frequency density 2.5, one 5 units wide with density 0.6. How many values in total?
- 3rd September 2006x = 70 and y = 36, each correct to the nearest whole number. Work out the upper bound of x - y.
- 4th September 2006The curve y = sin x° is drawn for 0 <= x <= 360. Write down the value of y when x = 360.
- 5th September 2006y is inversely proportional to x^2. When x = 4, y = 50. Work out y when x = 5.
- 6th September 2006The 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.
- 7th September 2006A bag holds 5 counters, r of them red. Two are taken without replacement and P(both red) = 1/10. Work out r.
- 8th September 2006On a histogram, a 4-wide bar and a 16-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 9th September 2006A car covers 580 m (to the nearest 10 m) in 5 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 10th September 2006A quadratic sequence starts 2, 5, 10, 17. Work out the second difference, and the coefficient of n^2.
- 11th September 2006y is directly proportional to x^3. When x = 2, y = 32. Work out y when x = 4.
- 12th September 2006In a circle theorem proof, a step uses the fact that the exterior angle of a cyclic quadrilateral is being found. State the reason being quoted.
- 13th September 2006The probability of winning a game is 9/10. A player expects 108 wins. How many games did they play?
- 14th September 2006A histogram has two bars: one 5 units wide with frequency density 0.4, one 25 units wide with density 1.4. How many values in total?
- 15th September 2006Rationalise the denominator of 40/sqrt(5), giving your answer in its simplest form.
- 16th September 2006Solve x^2 - 6x - 7 > 0.
- 17th September 2006y is directly proportional to sqrt(x). When x = 9, y = 27. Work out y when x = 81.
- 18th September 2006In a vector proof you find that vector PQ = 5a - 6b and vector RS = 20a - 24b. What does this show about PQ and RS?
- 19th September 2006A bag holds 2 red and n blue counters. The probability of taking a red is 1/2. Work out n.
- 20th September 2006On a histogram, a 10-wide bar and a 30-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 21st September 2006Simplify sqrt(75) + sqrt(3), giving your answer in the form a sqrt(b).
- 22nd September 2006Write x^2 + 10x - 11 in the form (x + a)^2 + b.
- 23rd September 2006A train slows steadily from 33 m/s to rest in 4 seconds. Work out its deceleration.
- 24th September 2006A cuboid measures 4 cm by 3 cm by 9 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 25th September 2006A bag holds 7 red and 3 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 26th September 2006A histogram has two bars: one 20 units wide with frequency density 1.5, one 20 units wide with density 3. How many values in total?
- 27th September 2006A rectangle is 18 cm by 16 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 28th September 2006Work out the coordinates of the turning point of y = x^2 - 14x + 10.
- 29th September 2006y is inversely proportional to x^2. When x = 3, y = 100. Work out y when x = 5.
- 30th September 2006A cuboid measures 4 cm by 6 cm by 11 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.