FDP on Elementry Mathematics

Arithmetic, Trigonometry Geometry and ​Algebra







-By. Dr. Dhaval Thakkar

Multiple Choice

Expand

• A

• B

• C

• D

Multiple Choice

Condense

• log₈(a¹⁸/b³)

• log₈(a¹⁸b³)

• log₈(a/b³)

• 15log₈(a/b³)

Multiple Choice

What is the value of x?

$$3^{\left(1+x\right)}\div27^{\left(3+x\right)}=9$$  

• $$\frac{5}{2}$$  

• $$-5$$  

• $$\frac{-7}{3}$$  

• $$7$$  

Multiple Choice

Evaluate $$1000^{\log_{10}4}-\log_464+25^{\log_510}$$  . Use the table to approximate the value of the logarithmic expression or use the change-of-base formula to simplify.

• $$161$$  

• $$61$$  

• $$-161$$  

• $$126$$  

Multiple Choice

Evaluate $$\log_330-\log_4\ 4^5$$  . Use the table to approximate the value of the logarithmic expression or use the change-of-base formula to simplify.

(Given $$\log_3\ 10\ =\ 2.0959$$ )

• $$1.9041$$  

• $$-1.9041$$  

• $$19,041$$  

• $$9,041$$  

Multiple Choice

The Pythagorean Theorem tells us that the relationship in every right triangle is

• $$a^2b^2=c^2$$  

• $$a^2+b^2=c^2$$  

• $$a^2\div b^2=c^2$$  

Explanation Slide...

The correct relationship in every right triangle according to the Pythagorean Theorem is a^2 + b^2 = c^2.

Multiple Choice

$$S^2=$$

• $$x^2+y^2$$

• $$x^2+y^2+z^2$$

Multiple Choice

The bottom of a ladder leaning against a wall is 1.5 m from the bottom of the wall. The ladder is 5.5 m long. Find how high the top of the ladder is above the ground, correct to one decimal place. 

• 5.2 m

• 5.3 m

• 5.7 m

• 5.8 m

Explanation Slide...

Using the Pythagorean theorem, we can find the height: h^2 = 5.5^2 - 1.5^2, h ≈ 5.3 m. Therefore, the correct answer is 5.3 m.

Multiple Choice

Choose the correct statements. (Select all that apply)

• The area of the coloured region is the same.

• The perimeter of the coloured area is the same.

• None of these

Multiple Choice

Your family wants to purchase a new laptop with a 17" widescreen. Since the 17 inches represents the diagonal measurement of the screen (upper corner to lower corner), you want to find out the actual dimensions of the laptop. When you measured the laptop at the store, the height was 10 inches, but you don't remember the width. Calculate the width of the laptop to the nearest tenth of an inch.

HINT: DRAW A PICTURE!!!!!!!!!!

• 7 inches

• 10 inches

• 19.7 inches

• 13.7 inches

Explanation Slide...

The correct statements are: Placing the squares side by side without leaving a gap will form a rectangle twice the size of one square. The area of the coloured region is the same. Both squares will overlap if placed on top of one another.

Match

Match the following

• $$\sin\ \theta\$$

• $$\cos\ \theta\$$

• $$\tan\ \theta\$$

• $$\csc\ \theta\$$

• $$\sec\ \theta\$$

• $$\frac{Opposite\ side}{\ Hypotenuse}\$$

• $$\frac{Adjacent\ side}{\ Hypotenuse}$$

• $$\frac{Opposite\ side}{\ Adjacent\ side}$$

• $$\frac{Hypotenuse}{opposite\ side}$$

• $$\frac{Hypotenuse}{Adjacent\ side}$$

Explanation Slide...

Multiple Choice

Elizabeth is flying a kite, which gets caught in the top of a tree. Use the diagram to estimate the height of the tree.

• 63.6 ft

• 1.59 ft

• 74.2 ft

• 86.9 ft

Multiple Choice

In the following diagram, the point R is the center of the circle. The lines PQ

and ZV are tangential to the circle. The relation among the areas of the squares,

PXWR, RUVZ and SPQT is

• Area of SPQT = Area of RUVZ = Area of PXWR

• Area of SPQT = Area of PXWR - Area of RUVZ

• Area of PXWR = Area of SPQT - Area of RUVZ

• Area of PXWR = Area of RUVZ - Area of SPQT

Explanation Slide...

The correct relation
Area of SPQT = Area of PXWR - Area of RUVZ

Hint: PQ^2+QR^2=PR^2 abd QR=RZ

Multiple Choice

Solve for the misssing distance

• 18.9 meters

• 19.5 meters

• 47.2 meters

• 27.5 meters

Match

find the area :-

½ × base × height

base × height

side × side

length × bridth

πr²

• ½ × base × height

• base × height

• side × side

• length × bridth

• πr²

Match

Match the following volume formulas to correct three-dimensional figures.

• $$\pi r^2\cdot h$$

• $$s^3$$

• $$l\cdot w\cdot h$$

• $$\frac{1}{3}\pi r^2\cdot h$$

• $$\frac{4}{3}\pi r^3$$

Volume formula for a Cylinder

Volume formula for a cube

Volume formula for a rectangular prism

Volume formula for a cone

Volume formula for a sphere

• Volume formula for a Cylinder

• Volume formula for a cube

• Volume formula for a rectangular prism

• Volume formula for a cone

• Volume formula for a sphere

Multiple Choice

Which cylinder will have a larger volume?

• Cylinder A
• Cylinder B

Multiple Choice

What's the volume of this sphere?

• 78.5 m³
• 392.5 m³
• 523.6 m³
• 62.8 cm³

Multiple Choice

Find the volume of the figure.

• 150.72 cm³
• 75.36 cm³
• 452.16 cm³
• 151 cm³

Multiple Choice

What is the volume of this complex shape?

• 28 cm³

• 336 cm³

• 304 cm³

• 32 cm

Multiple Choice

The arrow shown is on a sign. What is the area of the arrow?

• 17 in²

• 40 in²

• 52 in²

• 61 in²

Fill in the Blank

A water pump fills a swimming pool at a rate of 80 cubic feet per hour. A swimming pool measures 10 feet by 8 feet by 5 feet. How many hours will it take to fill the pool?

Multiple Choice

A quadratic equation $$ax^2+bx+c=0$$  has no real roots if

• $$b^2-4ac>0$$  

• $$b^2-4ac<0$$  

• $$b^2-4ac=0$$  

• $$b^2-4ac=1$$  

Multiple Choice

The values of k for which the quadratic equation $$16x^2+4ks+9=0$$  has real and equal roots are

• 36 , -36

• 6 , -6

• 6 , -7

• 6 , -8

Multiple Choice

For what values of k are the roots of the quadratic equation  $$x^2+k\left(2x\right)+2=0$$  real and equal ?

• 0

• 1

• 2

• 3

Fill in the Blank

Think of a number, multiply the number by 8, divide by 2, add 5, and then subtract 4 times the original number.

Multiple Choice

Divide 57 into two parts whose product is 680

• 11 and 15

• 17 and 40

• 9 and 4

• 23 and 28

Multiple Choice

Using your graph paper, solve the following system of equations.

• (-2, 1)
• no solutions
• (-2, 0)
• (-1, -3)

Multiple Choice

Using your graph paper, solve the following system of equations.

• infinite solutions
• (0, -2)
• no solutions
• (0, 2)

Multiple Choice

Using your graph paper, solve the following system of equations.

• infinite solutions
• (0, -3)
• (-1, -8)
• (1, 2)

Multiple Choice

1) Solve the system of linear equations.

• (-1, 5, 2)

• (1, -5, -2)

• no solution

• infinitely many solutions

Poll

How You feel this session......?